If I buy an IPhone 5 off of Ebay or any other website how would I activate it?

Could I choose any carrier I want or would I have to go to a specific one? If I can choose any which one do you think is the best at an affordable price?

For the least risk of trouble, you need the carrier that goes with the phone… For instance if you bought a Verizon iPhone you need to use it with Verizon. If you don't do that, there's a chance that even though the phone will work for voice and texts, it won't work with data.

Or, buy an unlocked phone, that will work with most carriers SIM cards.

As far as which carrier, Consumer Reports magazine rates best to worst monthly billed service carriers as: Consumer Cellular, US Cellular, Credo Mobile, Verizon, Sprint, T-Mobile, and AT&T. For prepay carriers best to worst it's TracFone, StraightTalk, T-Mobile, Verizon, Net10, Virgin, MetroPCS, AT&T. "Best" means reliable, good service, etc… Not necessarily cheap!

Probably not all of those carriers will work with a "bring your own" iPhone 5 though, so you'll either have to call them, or go to their store, or check their website.

P.S. The iPhone 5 is a 4G phone, so it uses SIM cards on all carriers - even carriers that used to be CDMA only like Verizon and Sprint.