Overall, when I'm in the mood for some uplifting, fun rock and roll, I listen to the Traveling Wilburys. I can get past the somewhat slick production because these are some genuinely catchy songs. Sure, it's not deep artistic progressive rock, but it is great songwriting. Although there are some memorable moments on their second release as well, Vol. 1, will always be the music of the true Traveling Wilburys in my mind, as well as just a fun album to listen to.
If this is your first real experience with the Traveling Wilburys, well, there really isn't anywhere else to start, as this was the only album with the original five Wilburys and in my mind it's far better than the second release. For fans and newcomers alike though, there has been a release of the entire Traveling Wilburys collection that includes both albums, a DVD and outtakes from the sessions that is worth picking up.