I have found some champions I am going to buy. I am summoner level 22 so I'm not that new at this game and I have quite a few champs so don't tell me to buy beginner champs(I have all but two of them). The champions I'm going to buy are as follows:

Champions:

ADC:
Alistar
Singed

APC:
Ahri
LeBlanc
Elise

Jungle:
Lee Sin
Amumu
Maokai
Shaco

Like I said I'm going to buy them all eventually I would just like to know what order I should buy them in. Thx. Plz don't be hatin.

ADC:
Caitlyn
Kog'Maw
Twitch

APC:
Gragas
Ziggs
Rumble

ummm? shyvana and amumu in APC? what?

yea youre REALLY new to this game

You are very new at level 15. Even once you hit 30, you are still new to the game. There is a lot to learn. I'd even call my nearly-800-games-played self relatively novice.

Like Eagle X D said, Shyvana and Amumu aren't AP Carries. Shyvana is an AP Bruiser and a Jungler. Amumu is an AP Bruiser, a Tank and a Jungler. Rumble can be an AP Carry, but is more often thought of as an AP Bruiser.

Of the AD Carries listed, I'd say Caitlyn is by far the most versatile and has an easier learning curve than the other two. Kog'maw can become a true force to be reckoned with when he gets a good lead, but has short range when his E isn't active and trouble staying relative if he falls behind. Twitch has huge potential but comes with a higher skill curve and less single-target capabilities than the others.

Of the AP Carries you listed, Ziggs is safer but, overall, I feel Gragas is the better champion by far.

Jax.

Shyvanna is a tank just btw Amumu can be tank or AP playing ap amumu is always funny.

You forgot:
Bruiser/top, Jungle, and Support.
You shouldn't just make a list and stay set. You're really new even at this point... I've been playing for 2 years, about 500+ matches, and I'm new too! Ashe is a good choice, if you own her. Here are my "best of" picks for the positions (a lot of these have some pretty steep learning curves, and require some practice... if you get to ranked, then most will be extremely useful... you'll be happy you learned them):
ADc: Corki, Ezreal, Draven, Graves, Nidalee? and Vayne. I would advise against Twitch... you might buy him later. Caitlyn's range can counter some ADcs... and Kog has incredible DPS, but requires some babying and skill.
APc: Orianna, Katarina, Elise, Morgana, Diana, Zyra, Annie, Ryze, Anivia, Ahri, Gragas and Akali.
Bruiser/Top: Darius, Shen, Malphite (possibly), Jax, Singed, Gragas, Yorick (a good Cho can counter), Cho 'Gath, Garen, Jayce, Nidalee?, Rumble and Lee Sin.
Support: Blitzcrank, Alistar, possibly Shen, possibly Nidalee, Nunu, Lulu, and Janna.
And Finally, Jungle: Amumu, Shen, Darius, Malphite, Maokai, Shyvana...
My opinion . Hope it helped.
(P.S.: I kinda used this to help http://www.reignofgaming.net/tier-lists/solo-tier-list )...

@Mich567:
That list is from before the pre-season changes. It's not entirely accurate anymore. Also, several of those champions require a higher level of skill then I'd recommend to anyone at level 15 (Orianna and Shen, for example). Recommending junglers to a level 15 is also a bad idea, in my opinion, since jungling, especially in the current state of the game, tends to require a full rune page.