That's two different questions I think ... all of them are "worth a listen" but as far as "essentials," I say Blackout and Meanest are the best.
Live on St. Patrick's Day is awesome too. It's mostly a repeat of album material, of course, but original lead singer Mike McColgan left after the second album, replaced by Al Barr, and since Live came later, it has "alternate" versions of some of these songs with Barr instead. There are also some covers like "Fortunate Son" but I don't know how many of these appeared elsewhere.
Warrior's Code is great and a little more "traditionalist" than straight-up punk.
Sing Loud, Sing Proud is pretty good but not AS good. It does have a few really great songs though and is definitely worth a spin.
Sorry to say I'm not very familiar with their first two albums or with the singles collections.
Studio albums
* Do or Die (1998)
* The Gang's All Here (1999)
* Sing Loud, Sing Proud! (2001)
* Blackout (2003) (#83 US)
* The Warrior's Code (2005) (#48 US)
* The Meanest of Times (2007) (#20 US)
Live and compilation albums
* The Early Years (1998)
* The Singles Collection, Volume 1 (2000)
* Live on St. Patrick's Day From Boston, MA (2002)
* Singles Collection, Volume 2 (2005)
