I am personally considering to build my own computer (don't know if it's sooner or later) that is dedicated in being capable in doing some high level video and visual editing. I am currently editing using my laptop and it's not an editing/gaming computer and it's been doing fine, but I noticed that it wasn't going smoothly when I am trying to do editing and After Effects at the same time, and I think it would benefit me to have a computer to be able to handle those at the same time.

So how should I approach the build of this computer in order for me to do these things (and also play some of the more demanding games if I get some) and doing the normal things like Windows Office applications, while not absolutely breaking the bank? I know building my own computer is cheaper than to buy a premade one, that's why I'm considering this approach. What parts are the best that I am able to get or should I focus on more with my budget?

Here are the software that I already own/using and am planning on using for this computer:
Sony Vegas Pro 12
After Effects CS6
Hit Films 2 Express
Photoshop Elements CS 5

Hopeful budget: $1200~$1500 ($2000 will be pushing it and no more than that) for the desktop only

An upper band of $2k? Man, you have no problem. In your money I must have soent about 1, 300 and I have a great build.
Since you're main focus is editing the most important thing us the processor. I went for an intel i5 which is plenty good, but if you are seriously on doing heavy editing you might as well get an intel i7, 4th gen not 3rd (thats a non negotiable, dont get a 3rd gen processor ).
Also needed is RAM.
You want to get DDR3 Ram, at least 8 gigs, its not all that expensive though, so you could go for 16 if you wanted.
You need a motherboard that supports both DDR3 RAM and 4th gen intel processors too.
As for gaming, that depends on what you play. You coukd get a motherboard with on board graphics that could play most games fairely well. Unless you are playing taxing games in which case you would want a dedicated graphics card.
Id recommend an nvidia card over an amd.

Id also recommend using an ssd harddrive for your applications and operating system, it massively boosts system speed.
Beyond that you only really need to worry about getting a case and power supply.
The case will be either semi or full atx, which corresponds to the motherboard. Small (micro atx) motherboards or full atx (large) motherboard support.
You need to make sure the case is big enough for the psu, graphics card and motherboard.
The psu has to be large enough to supply all the components you have. 650 watts would probably be more than enough but you can use various websites to calculate how much you need.

I realise much of what I said (ddr3, i5 etc) may not be clear to you, but if you are wondering about the difference between i5's and I7's are, or DDR3 and DDR2, theres plenty of web guides. Or you can ask me whatever questions you may have. Either or.

thenumberone : Lol, I know what you are saying when it comes to those terms. What can be confusing for me is if we get wayy too specific in the model number or different products with similar name or comparisons between different brands, etc. For example, when you say the latest generation of intel i7, there are actually multiple choices of i7 processors but are different. I have done some research on this, and some of the stuff that you are saying is very consistent with what I'm seeing. I just want to see if anyone hear can give more clarity on that.

Yeh I know there are specific models etc bit thats not what the generation refers to you.
Example.
I have an i5 4440. This comes as 3rd or 4th gen.
The advantage in getting the 4th grn verdion is that they have squeezed more juice out of it. You get more power and it uses less energy. The main benefit of that is it wont get as hot as the 3rd gen.
The feature that is great about i7s, id hyperthreading. Thats something the i5s dont do, and if you are going to do a lot of data crunching, it will be indespinsible.
That being said, an i7 isnt necessarillt better than an i5.
I have a 4th gen 4440, which runs at 3.10 .ghz and has 6mb cache memory.
Thats better than a lot of low end I7s, which is wht I got it. On your budget though, id go for an i7 that clocked at least 4ghz.
And also make proccessors that tend to be cheaper, but intel are the market leaders and tend to offer a smoother performance.
The question is how much you are willing to pay for the processor alone. The i7s go from decent to insane in price.
That being said, on your budget you could afford it.
If you look at intels website you can specifically browse 4th gen i7s and see the differemces vetween the version (noteably core and thread number, power drawn, max running speed and cache size).
Unless you are doing pretty intense graphical edditing its unlikely you will need an amassing i7, but theres also future proofing so you can brong that into consideration.

Frankly, given youre stated intentions, the processor is the highest requirement and youre probably wantimg to soend at least about $220.
Do you have any idea what kind of performance level you want in regards to the processor? And are you planning on running dedicated graphics or using the cpus integrated graphics system?

thenumberone : I am hoping to run more graphic intensive projects with the use of after effects, so the processing I hope would make my editing to be smooth so that I won't need to lower the quality a lot further in order to put the clips or the components together, or seeing the laggy image appearing on my screen when I want to check frame by frame footage. So I don't know which one that you said on your last sentence would be more likely to help me do that.

play4fun :
CPU is needed for most rendering, but with the advent of better hardware/software design, many apps can utilise the graphics card as well as the cpu.

All you're listed apps utilise the GPU(although the photoshop one is somewhat ambiguous. Most versions dont utilise the gpu much, but apparently cs5 does. How much I dont know).
Basically if you get a good gpu you dont need a top notch cpu.

There is an AMD V Intel debate going on, but most people agree for rendering, intel is the choice.
And again, i7 has hyperthreading, allowing each core to essentially double its instruction handling capacity.That doesn't mean double performance, but its often a nice boost.

The best i7 would be the extreme, but frankly, its too expensive. It comes in at around $770-$1,300, and I don't think you are getting much extra for those dollars.

The much more reasonable i7 4790k Is a great piece of kit, and comes in at about $350. Its there best (none extreme) 4th gen i7 out just now, and I'd happily buy it myself if I needed the extra 'juice'. That price really isnt bad, I paid about $170 for mine and it was an average I5.
http://ark.intel.com/products/80807/Intel-Core-i7-4790K-Processor-8M-Cache-up-to-4_40-GHz

Even a lower end i7 would probably do the job if you wanted, though you wouldn't be making massive savings.
You could save maybe $100 getting a 3rd gen i7 (i linked 4th gen) but I really think that would be a terrible choice.

i7 4790k has integrated graphics too, the same as my i5 has. If you are planning on playing medium to advanced games though, you would probably still benefit from getting a mid range gpu. It would also aid your rendering, but it shouldn't be an immediate necessity if you want to hold off.
At any rate, you can get very decent graphics cards for very little money, so you can feasibly come in under your lower budget if you want. I spent about $400 on my graphics card, but that was a seriously ott card, and I really dont imagine you needing it. The single largest cost in a build are the cpu and gpu, so you can afford to make a pretty good build with your current budget.
I spent around $1370 on my complete build, using pretty top end products (apart from the cpu). If you chose a similar setup (in reality you will probably spend less) you would come in around $1,500. Assuming you get a mid range graphics card, it could be around 1,200. Buying that from a shop would be closer to $2,000, if you were 'lucky'.

play4fun :

http://pcpartpicker.com/p/7ntYhM
cpu I chose because it is basically a 4770 but  a bit cheap
motherboard I chose because mobos don't affect performance  and asus is makes great products
ram is because it is the cheapest per gig 16gb  kit
storage I chose the hard drive because it had the best price per gig and with photo shop and editing you can eat up on hard drive quickly and the ssd is a for fast access to projects you are currently working  and also you os and programs

case well basically it works and nzxt makes good case
psu it has a bit more than you need for power and it is 80 plus gold so it is more power efficient

You'll be wanting an i7 not an i5 for maximum performance if the cost between the two isn't too bad. The more cores you can get the better. Quadcore would be find but if you can get a 6core CPU you will notice the difference.

RAM, DDR3 is fine, don't really need DDR4. 16gb minimum I would say. Though RAM is cheap these days. A cheap kit I usually use is some gskill ripjaws.

For GPU you'll want to go with nVidia. I believe most of the programs you listed utilize CUDA (nVidia only) but it'd all depend how the software has matured over time to support OpenCL (which is on both but I believe AMD has a better implementation, but don't quote me on that).
You'd have to do research into this to see what the specific programs you use work best with.

As others have said, SSD for your OS and programs. You'll want to then have some regular HDDs for mass storage. Maybe in RAID depending if writing a render to the disk is where your bottleneck may be.

But in saying that, something like an i7 2600K, 8gb RAM and a GTX680 won't stop you from editing videos, the more money you put into it the less time rendering will take. Pretty much is a time vs. money thing.

Here is a video I watched some time ago which goes into a bunch of different details about why they chose what they chose. I'm sure there is some more videos on their channel which talks about some of the same topics.

I didn't read every word of the whole thread, but here is what I'm thinking:

CPU: Intel i7 4790K - $336. Good high-end bang-for-buck choice.
Mobo: GIGABYTE GA-Z97MX - $130 . It's well priced, it's has good reviews, will serve all the other components well.
RAM: CORSAIR Vengeance 16GB 1600 - $150. Usually I always tell people they DON'T need more than 8 GB of RAM, but in your case, large videos take a LOT of RAM, so be safe with 16 GB. Also this is 1600, meaning it's not only a lot of RAM, but it has a good speed.
HDD: HGST Deskstar NAS H3IKNAS30003272SN, 3 TB - $130 . I think 3 TB should be a good start, but you can always add later. You may be interested in a Solid State and HDD combo, so see below. Also, this is 7200 RPM, meaning it's not "green" and powersaving friendly, but it will deliver on speed (as far as HDD in that price range go).
Case: Rosewill BLACKHAWK - $85. Wow for the price, it's large, has 5 fans, and sturdy (I've build using this one before)
DVD/Bluray: LG Black WH16NS40 - $60. Assuming you want Bluray burning capabilities. If not, you can get a cheaper DVD only burner, but still not a huge price difference.
GPU: AMD FirePro V4900 100-505844 - $145. This is where other users will want to tar and feather me. I did not recommend an 'awesome gaming video card'. This is called a "workstation" card, meaning it's for professional use, meant for editing HD and 3D and has really stable drivers. If you want a more "gaming friendly" card, there are lots to choose from; we can help you with that too.
PSU: XFX XTR Series P1-550B-BEFX 550W- $80 . Way more watts than you need, but you never know what you might want down the road, like a gaming PGU. I love XFX, as they are made by Corsair, and this one is modular (way nicer to set up) and gold rated. Don't ever cheap out on a power supply.
Card Reader: ORICO USB 3.0 SuperSpeed Multi-Card Reader - $25 . Just a USB 3 card reader.
OP : Windows 7 Home Premium - $100. Many people still find 7 to be more stable and easier to use on desktops, myself included. 8 was intended for mobile, and then shoved onto desktops clumsily.
Grand total = $1241 including shipping for the most part.

Other things to consider: monitor... though I will leave that up to you, as you likely know what you want.

SSD: You may want an solid state drive as well. I'm not sure how much you know on this stuff, so I apologize if I insult you. SSDs are very very fast, but much more pricey. They are great to install your Operating System and programs on it, but I would not recommend storing your videos and audio on it, unless you really want to go all out on price. So if you are interested, here is a good example of a 240GB one, costing you and extra $100.