What's the best place to start? A-Sides Win? I've liked everything I've heard from them on the Best Show.
I would say get One Chord to Another and Twice Removed.
Then get Never Hear the End of It and Navy Blues.
Then get Parallel Play.
I'm not the biggest fan of Action Pact or Pretty Together, I haven't heard the new EP or Between the Bridges, the first album is them trying to be super "alternative" (Smeared is not bad, just dated. The song writing is still pretty strong, but not everyone had found their voice yet), and the live album isn't anything essential.
I voted for Twice Removed and then realized I like One Chord... more.
If I may, I'd suggest OCTA, NB and TR together. They are really great all together like that.
Then I'd go for NHTEOI and PP together - NHTEOI is so unexpectedly good, and then PP is like a kick ass B-sides collection accompanying it.
PT has aged better than I ever expected it, but there are clunkers - it's their McCartney II.
And, if you can, try to get the double disc One Chord - their "Beach Boys Party" disc is really really a lot of fun.