It's a pretty simple question, really, Nya~.

But, still, which difficulty do you try out first for most new games? Are you the type that just goes on easy mode to give it a first time try, or are you more advanced and capable enough to tackle down the harder challenges on your first time?

I try for the slightly more challenging modes on some games, and even most times hard mode. Though, for certain games such as MegaMan, I'd go and try it on easy mode first, given the option is there, Nya~.

If I am familiar with the series I will pick hard. If I am starting out I will pick normal or easy. If I have never heard of the series but someone tells me it is very difficult, I always pick hard just to see if I can do it.

I always play "normal".
Always.
I never play easy mode unless I need it to unlock an item or feature or just finish the last achievement award.
If I love the game I will give it a Hard or Extreme mode go.
Like "The Legend of Zelda 2 Shadow of the Night". or "Onechanbara". or "Devil May Cry 3".
I normally do not select easy due to all the lessons from earlier games not giving away the ending or sometimes cutting out a few levels plus the ending. If I select hard I may do fine starting out, but a few days or weeks go by till I pick the thing up again and I forget the control scheme and I get brutalized to the point of needing to restart and go with the normal mode anyway. Some games thrive on high difficulty.(Ninja Gaiden, Strider). And others are painfully easy it just takes endurance or concentration. (Tetris, Gauntlet). I really do not see the need for extra difficulty options in games other than bragging rights.
Saying you toppled any game on hard mode is kinda silly.
I still have respect for folks that have to take on all games in hard mode. I do it too.
But I honestly do not see the idea of saying "I beat Dead Or Alive Beach Volleyball on hard mode" as being anything that can be marveled at.
Good Luck To All.
I'm done. Stick a fork in me.
Peace.

The first two times I play the game, I always go for Hard mode, just below Expert or Veteran, just so I can get a feel of the game, and get the hidden things/achievements so I can play it on Expert the third time without anything to get and know what to do.

normal mode.
On easy you can't get the full depth of the game.
On hard you move so fast you miss little things.
If its a great game il complete it on hard mode.
Like hitman bloodmoney. On easy theres no notoriety, evidence or penaltys and you can see every npc on your map, plus 7 in game saves.
On medium its 3 saves and notoriety, plus penaltys. You only see civilians and targets on your map.
Then theres hard. No saves. Notoriety in effect. Penaltys. Evidence effects rating. Only targets appear on the map.
If you play easy, you miss half the stuff that makes it interesting. On hard, well failing repeatedly can really kill the fun. You play on normal and you learn the controls, you learn the tricks of the game, the setup of the levels, and if its fun you can carry that experience to the next level.
If a games good you will likely play it twice anyway so you dont need to jump in at the deep end right away.

I Usually go on Easy Mode When Playing New Games, Just To Try To Get The Hang of It until I get to the harder levels.

Easy because I wont know how to play the game and it is already hard has it is. 

Depends on whether I've played a game in the series or not. If I have, chances are I know the controls and patterns that occur throughout the series. Usually, I totally ignore easy, and go straight to normal. Sometimes, like with the new Fire Emblem, I'll jump into hard though.

I figure the game was "meant" to be played on normal or medium mode. So I'll play it that way, the most normal way to play.

As many people before, I then play hard a second time around if I really like it.

Now if there's a big verity, like: Beginner, Novice, Easy, Amature, Adept, Experienced, Hard, Insane, Instant death. Then I will pick the slightly hard side of the medium range.

I play easy on almost all games I play, because i'm a novice at alot of genres. But, if there's a game where easy is TOO easy, like mua2, I pick normal.

I usually do Normal. So usually, the 2nd out of 3, or 2nd out of 4. Sometimes I will be bold and go 3rd out of 4 difficulties, but I rarely ever do that.

Depending on the kind of game it is, I'll start on easy, then move onto normal. Next, I usually go back to easy, but try to make it hard by doing something that would make it hard, then I move onto hard. Or if there are three different files, I'll just have one difficulty for each file, and just play whichever one I feel like playing. 

I usually start off easy when I'm playing a new game, then up the difficulty as I progress. 

Normal, I always start at Normal.

Then, when finishing the game on that Difficulty, I go for the Harder modes.

Well I wouldn't really say it means one isn't capable if they start with easy. I myself don't see a reason to skip straight to harder modes. I figure the game should be fun enough on easy the first time. If it isn't, it isn't fun enough for me to waste my time on in the first place. I save the harder levels for replay. And I won't lie, I would probably get my butt kicked if I started out on hard in a new game. lol However, I would be willing to start on a higher level if I was used to playing a game and I got the sequel. Otherwise, I'd give it a play through on easy first. But to each their own, eh?

I learn games really quickly, so I start on medium.

For me pretty much when its a first time playing a game most people go easy like me but usually I go up then 3rd time all out and make probably some obstacles to make it harder