Generic starter advice- It depends what you want to do with your points and what carrier you prefer, for example if you're near a Delta hub like Atlanta they might be your best bet, Dallas is American, etc. It also depends on where you want to go (United probably most flexible, second is AA and they're the best to South America, and Delta is dead last though may be the best for Australia).

My opinion if you're just starting is to double team it with Chase cards. If you have a Chase Sapphire Preferred (or either of the Ink Cards) you can transfer Ultimate rewards points to United (Star Alliance), Korean Air (Skyteam), British Airways (Oneworld), or Southwest (no alliance but I believe you can use points on Airtran as well?) as well as Hyatt, Priority Club, Mariott and Ritz-Carlton Hotels if that's your thing.

That way you can transfer rewards to all three major alliances (you can use the points on allied carriers). So if you fly Delta sometimes but use United usually, if you have a Chase Ultimate Rewards card you can transfer your points to United usually, then if you want to book awards on Delta all of a sudden you can just transfer to Korean and use their miles on Delta.

The reason I'd recommend Chase over other multi-partner points (Amex Membership Rewards) is because you could wait a month after getting a Sapphire Preferred (or Ink, or Bold, all three waive a first year fee), you can apply for a Chase Freedom card which offers 5x points on certain categories every three months (gas and drug stores this quarter). Then you can transfer to your Sapphire Preferred (or Ink or Bold) account and transfer them out again. That ONLY works (Freedom to Sapphire Preferred) if you have one of those paid cards, though.