how do you know which ones dont have/use mana in the store?? (i'm TERRIBLE at mana management)

I literally just googled the title of your thread and it came up with a list for me.
Google is your friend.

If you look at the cost for their abilities, and it says Energy, they are Energy champions. If none of their abilities have any cost, they don't have any mana but longer CD. If their abilities cost Health, then they rely on large health pools to continue to use abilities.

None of these types of champions are mana based champions.

finally found a site with the answers i needed, you for the idea and heres the list for anyone else looking akali, dr.mundo, garen, katarina, kennen, lee sin, mordekeiser , renekton , rengar , riven , rumble , shen , shyvana , tryndamere , vladimir , zed.

now the hard part..which ones to get..already received a few as gifts. i have : garen, rengar ,riven, rumble, tryndamere. should i try any others? i have plenty of RP from Christmas just not enough for all of them^^

Zed is pretty fun in my opinion, but people say he's hard to use. If you're up to the challenge, he could be a fun champion that doesn't use mana.

You have all those champions and don't like any of them? I'm new to the game, and found Garen very easy to use. He's tanky but if you build him right, he can do decent damage. At this point, he and Xin Zhao are the only two I've bought.

to Delingar ..i actually like most of them..Rengar is my favorite of all the champs i have played, but he is only good for ambushing weakened players for most of the game, and getting items and xp on him is super hard..what i have been reading says he is due for some slight buffs in the next patch..i hope its soon..and i need a top /mid lane champ (im terribad at jungle). mostly i keep looking for a champ thats fun for me like Rengar is but not neutered in power. my goal is to find and buy 3-4 champs that i can be good at.