Twisted Metal 1, 2, Black, and TM 2012
It looks like Twisted Metal 1 and Black weren't the only ones joining the fun, as the PSN is getting an all-out four game birthday pack for $39.99. Should you decide to go with the piecemeal approach, the new 2012 Twisted Metal game is on sale for $29.99, 1 and 2 are going for $4.99, and Black is $7.99 -- it'll be running for one week from today.
For all you mathletes out there, that's around $8 saved through the bundle.
If you're looking for recommendations, Twisted Metal 2 and the new iteration probably hold up the most, as both have tons of variety, and solid mechanics to boot. Although the first game will always be dear to my heart, it's aged a lot worse than 2, so your mileage is going to vary there.
As for Black, it's still a pretty awesome game, but the single player campaign is a bit weak -- but really, you can't go wrong overall.
Twisted Metal [Sony Blog]