Braum or alistar

You can get Alistar for free through Riot's promotion on Youtube. The process is actually broken, so you'll need to submit a Support Ticket, but Blitzcrank Bot will get it to you instantly.

There are 3 you can get from the promotions that are always running, and Amazon is currently giving away the entire Champions Starter Set if you connect your League account to an Amazon account (that offer ends tomorrow). Check out the links below.

https://support.riotgames.com/hc/en-us/articles/202083184-Promotional-Content-Free-Swag-

http://na.leagueoflegends.com/en/news/community/promotion/link-amazon-and-unlock-free-starter-bundle

What DT Nami said

Both are favorite champions of mine; I play Braum more in ranked since it's easier to mess up as Alistar (although they are changing him so his WQ is much, much easier to land). Both do different things; I think Alistar is a bit more flexible in some ways (he has both engage and disengage, has sustain in lane with his E, and his ult is incredibly powerful), Braum is a bit more niche (is a solid support throughout, but he really shines on teams that can make use of his passive, ie. auto attack a lot, and really works well against heavy ranged teams, especially champs like Ezreal).

Alistar hands down. He's more unique of a champion. If you roam with movement speed, flash, and ghost setting up ganks early game majority of the time you win.

He's good at top, mid, and bot. The only thing that doesn't work well in all matches with Ali is stacking attack damage.