As far as trying to pick up songs by ear, you and I are probably in the same boat; however, I'll share what is helping me get better.
I don' t know that there is a one progression that is greater than other; however I would say, if someone put a gun to my head, that a 2-5-1 is probably the most used progression. Now, what I have come across is that there are various ways to play a 2-5-1 progression (i.e. tri-tone substitution), and that's what's baffling me at the moment.
I hope this helps, be blessed
Jonathan