If you have a credit card - might as well get an airline card! My favorite is Chase United! They offer 40,000 miles to start which is amazing! I bought a flight to Italy for 30,000 miles (so that is an example of how far that many miles can bring you).
I know what you are thinking - this is going to take years to build enough miles to fly for free - so what!? Plan ahead! If you get a credit card today - you will be flying for free in a year from now!
I usually fly United because I live in NJ and Newark is mostly United flights - I get miles with my MileagePlus account so I build up these miles fast between the credit card and flying! Chase also has other great Credit Card options that you should look into! Other options are American Airlines, Delta, and American Express.
P.S. If you don't have an airline credit card - or you do but you also fly other airlines as well - make sure you are signed up for their frequent flyer account! Even if you don't have a credit card you still can sign up for free and you can start racking up all the miles you fly!