Can't speak to the Online version, but I bought Black a couple months ago. I've also got Twisted Metal 2 which was excellent. I love Black as well. If you like to blow up animated vehicles with some really sick storylines, you're going to love it.
I don't think the Twisted Metal series will ever recover and make it back to the heights of part 2 (one of the best games for the Playstation), but Black is at least way better than parts 3 and 4. They were big missteps.
On its own terms, Black is pretty good, though. The online version plays a bit like an old Quake deathmatch most of the time, but I couldn't quite figure out how to set up a room for one of the other game types and keep it open right (so people could join and start a larger game) when I had it. I haven't actually played it in a bit, I'll have to give it a shot again. Once you try it, I'd be interested to hear which modes you think are the most fun.
Haven't played Online...but plain old TM: Black is a good game. IMO, The pinnacle of the TM series is and may always be TM2, though. Just had everything going for it: Crazy Gameplay, varied and creative levels, and a sense of humor sorely missing in TM: Black.
Not to mention those kick ass comicbook-ish cut scenes! Fit the game like a glove...I really wish they'd go back to them.
When you say you sent off for it, was it from an ad somewhere in TM:B or the PS2 online kit or somewhere else entirely? I don't have the online kit, but I do have broadband and may get one when they come down price-wise.