Where do you live and where do you fly?

If you live in the US and fly domestic you out of luck as far as lounges go, as they count on passengers to to buy an annual membership. (Can anyone chime in on Alaska Airlines?)

The higher the status, the lower the cost of a membership.

Now if you fly international I would say AA is the best. Why? You can do a PLT Challenge and after one TATL, done right, you have access to OW lounges. Access is granted when you fly on a OW itinerary. (For access in the US on the day of international travel*.)

I lived in Europe and as a PLT/EXP loved using the OW lounges in MAD, LHR and MAD and others on inter-European flights. When I was in the US I could not use OW lounges unless I was headed back to Europe. (Or any other longhaul international destination)

Since your goal is lounge access, there are other ways to gain entry, such as Priority Pass and carrying the right credit card. I'm sure someone will be along and tell what those cards are, I'm not exactly sure myself.

*International does not include most North American flights.