Here's the leaders and their advantages:

 GYM LEADERS

 Pewter gym - Brock - Rock-type

 2 words can describe Brock's battle: free exp. All you need is to use your starter:

 Charmander: if you chosen charmander level him until he learns iron claw, then just use it, but be careful for rock-type attacks
 Squirtle: kind of obvious, keep using bubble and it'll be quickly done
 Bulbassaur: leech seed them, after it keep using razor leaf
 
 There will always be room for a mankey after all fighting-types have advantage against rock-types, and be sure to defeat the camper so 
to get some support xp, after beating Brock you get a badge and a TM

 Optional:

 If you're starter is not bulbassaur, be4 going to cereculean try to catch a pikachu

 Cereculean gym - misty - Water-type

 First of all move pikachu to the front of the team, you will notice that the gym is full of swimmers, keep using pikachu and as long as he's ok keep it, then start a battle with misty, defeat her first pokémons and when she's about to use her last pokemon set out butterfree/beedrill so you can try to poison/confuse it and quickly finish her, if it don't catch any status abnormality just keep the electric strategy, soon starmie will faint, and you'll get a badge and a Tm as a gift.

 Vermilion gym - L.T. surge - Electric-type

 He might be challenging according to your Pokémon, if you chosen bulbassaur use him, charmander also can easily beat him but if you chosen a squirtle, try using different Pokémon you got on your way such as ratata, meowth, growlithe, etc. After he send out raichu try everything, and when I say everything I mean attack like crazy cuz there's no time for lowering random status, after all it have monster status, but keep your head calm, and don't forget to get your rod in the town. After defeating him you'll get the badge and a TM.

 Optional: catch a spearow if possible

 Celadon gym - Erika - Grass-type

 If you do not own fire types such as charmander or growlithe try the bird types such as spearow, this gym is fairy easy, all the ladys inside will use grass pokemon so do not be surprised if it takes only 5 minutes, after reaching erika use all you might and focus in killing vileplume the fastest you can, and be careful with tangela he will also be quite annoying. Once again a badge and a TM

 Optional: catch an abra and a bellsprout for future battles

 Fuchsia gym - Koga - Poison-type

 I highly recommend you to use a venonite or a magnemite (if you have one) if you don't, try finding an abra and raise it, the gym will be practically a maze with skilled trainers, if you raised abra properly it'll envolve and use psychic attacks which will be extremely useful, both kadabra and butterfree can learn psychic moves so after reaching Koga be sure to put them in the front line, and watch out for muk, he's poison is really annoying. Badge and TM


 Saffron gym - Sabrina - Psychic-type

 Once again use bugs with bug moves, because bug moves have advantage (note that caterpie will learn bug bite if kept from envolution) also catching a ghastly is NOT recommended ,after all he's also a poison type who's weak against psychic, which makes bug pokémons the last appeal, and keep in mind that bulbassaur, oddish and bellsprout are also poison kinds, which makes them weak against psychics. Use the teleporters to reach sabrina, there was a pattern which makes you avoid all battles but I don't seem to remember right now, but anyway, she'll be quite easy just be extra careful against alakazam or else. Once again the badge and TM

 Cinnabar gym - Blaine - Fire-type

 As cinnabar is surrounded by water, use the good/super rod ad use the water kind you find if you all ready don't own one, ground and rock Pokémon are also recommended, if I'm not wrong the gym is also filled with poison trainers so use alakazam if you have him, battling blaine will require lots o' potions, the only real challenge will be the arcanine, he'll make you want to throw rocks in your pc, or at last I did wanted but anyway, if you have the same problem as me, that one that makes you use gyarados in EVERY pokemon game, he'll learn hydro pump, which will turn into the key of the victory. Ooonce again badge and TM

 Optional: go to seafoam islands and get a cloyster, he's ice moves will help lot!

 Viridian gym - Giovanni - ground-type

 Simple, use water, grass and ice to get advantage, kind of simple. Defeat all the trainers and blah blah blah and challenge giovanni, lol you're now battling the team rocket boss O.o, he'll be washed away in no time. Badge and TM, why am I wring this anyway? Oh well, after beating him You should prepare yourself to the ELITE FOUR:


 ELITE FOUR:

 IMPORTANT: the elite four is 5 consecutive battles, and if you followed my team suggestion (you crazy man) your team will be:
 Starder, raichu, victreebell, kadabra, fearow and cloyster, this team will surely pass trough the elite four:

 First elite - Lorelei - water/ice-type

 Everyone claims she uses ice type, so you will fill yourself with fire ones but keep in mind that her Pokémon are ALL WATER TYPES mixed with ice (except jinx), so fire type are totally off, try using the team i reccomended: Use raichu's eletric tricks and she'l have o option then rethreat, be extra carefull with jynx, as he have some overpowered moves

 Second elite - Bruno - fighting/rock-types

 Bruno uses both rock and fighting Pokémon's, use victreebell's grass moves against the onix ad use kadabras's psychic moves at the fighting ones, might take more time then expected.

 Third elite - agatha - ghost/poison types

 Just use kadabra to get advantage, after all every of her pokemons are half poison, if she uses ghost moves be sure to recover hp quickly

 Fourth elite - lance - dragon-types

 Cloyster's iced moves will take them out quickly, there was SOME time since I last played so I think he have a gyarados but I'm not sure, use raichu in case he do have it

 CHAMPION

 Champion - Gary/blue- lots

 I don't really reember his team but i think it was nidoking, ryhorn, alakazam, victreebell, ninetails and the "opposite" starter, if tes use alakazam against nidoking and victreebell because of the psychic advantage against poison and fighting, victreebll (your) agains ryhorn due to it's weakness against grass, use cloyster againt alakazam as he'l do regular damage in it and also against ninetails because he's also a water type, and finnaly go for the starder:

 if his starter was bulbassaur use fearow/alakazam
 If was squirtle use raichu/victreebell
 If was charmander use cloyster/raichu

 Soon you'l beat him and every1 will have a happy end, exept for the families of the pokemons you bruttaly murdered while training

 I'm sorry for not adding muck details to the elite 4's, all i can say to you is:

 G-o-o-d L-u-c-k

I like it but you could have done a lot better. It is very short, so I suggest that you try to add more detail and make it longer.

@zanderlex I already edited it and now it's more complete, thanks for the hint

Quite a few nasty typos. Who's Venonite, for starters? I bet you you meant Venonat, right? Anyway, make sure you make your guide easy to comprehend to others by haviing your spelling as clean as possible.

Your advise is legit, though. Other than the spelling, I don't see anything wrong with this. Good job.