I want to buy some modern LP's from some bands (The National, Gaslight Anthem, Elvis Costello, etc...) and was wondering where to start?

Should I buy a Record Player or a Turntable?

Would the speakers on the record player go out pretty quick, leaving me needing another one?

Would either of them play all the different sizes of records, or would I need to buy special attachments?

Would they both be able to play older records if I picked some up at garage sales?

What are some good brands, should I go used or new, do turntables have something where I could plug speakers into?

I am completely clueless when it comes to this topic, but am itching to start collecting them. Thanks!
Edit: Like for example; what if I bought a turntable that had a speaker jack, and then bought a little guitar amp. Would this work?
Like something like this:

http://www.amazon.com/Sylvania-SRCD873-Radio-Turntable-Silver/dp/B002UXHXUU

With type of amp:

http://www.guitarcenter.com/Fender-Mini-Deluxe-Amp-480704-i1145406.gc

?