Twisted Metal, my love. The first game is what made me really want a PS1, glad I ended up getting one. When I broke my arm I had to play 1&2 by using my chin to steer the car with the D-pad. Good times. I could ramble on about the series for hours, but I'll keep it to the topic.
As far as gameplay goes, 2012 is my favorite. I just feel like it's the best balance of all the different gameplay styles in the series. It was also the most fun I've ever had in a PvP online game. To bad the online died a quick and not very graceful death. You can still play it online, but hope you enjoy getting stomped by people who've kept up on playing it for 13 years. It also has a fun co-op campaign that I've dragged all my friends through! I think the biggest downside are the boss fights after The Brothers Grimm. They're fine on lower difficulties, but if you're going for all golds on Twisted to get Warthog, you're in for a bad time. The final racing level is also kinda shit. Head-On and Black take second and third place. Head-On is the slowest of the three, but still fast enough to feel exciting. It also has a fun co-op campaign. A bit on the easy side though. Black felt the closest to 2012, but the game was the most brutal of the series. It also has a co-op campaign! See a pattern here?
As far as story and endings go, gotta go with Black. The game's atmosphere is just fantastic and it had a good cast of interesting characters and motivations. Though as mentioned above, it really does come off as a bit edgy. x) For it's time it was pretty dark and twisted though. The censorship was really weird though. Not being allowed to swear was strange in an M rated game, but I guess they had reasons? I also remember them changing some things from interviews in magazines before the game's release. The one that I remember best is how they changed Dollface's story from it being her dad who put her in the mask to Mr. Kreel. Of course there's the famous removed scene of Preacher drowning the baby in the baptismal water too. 2 and Head-On take second and third place. The feel of 2 was never quite matched, but Head-On did a admirable job continuing the story.
Next, the music. This is a super tough one. Even the lesser entries in the series have a bangin' soundtrack. Black will not be the winner, but it does deserve mention for it's amazing menu music and really good use of Paint it Black. I think I'm gonna have to go with the soundtrack from 3. It's only two bands, Rob Zombie and Pitchshifter, but 3 was the game that got me into them and while I prefer White Zombie over Rob Zombie nowadays, Pitchshifter is still a favorite. 2 and 2012 would be second and third place. 2 doesn't have licensed music and it frankly doesn't need it. It just has a banger soundtrack. 2012 has a nice mixture of licensed and original tracks.
Car and level selections are up next. I'll have to give this one to Black. A good mixture of new and returning cars and a good selection of levels that go through some really cool changes and have some nice secrets. Head-On and 2 for second and third. Head-On has a good car selection, but nothing new except for Cousin Eddie and, uh, ATV. If you have the Extra Twisted Edition you get all of Black's cars and two new ones too! Though Gold Tooth is just dumb and lazy. It has a good spread of stages set around the world and I like being able to choose between levels. 2 did an excellent job at expanding on the first game in every way. A good car selection and some really good and memorable stages. Apropos to nothing, Warthog in Black and 2012 is my favorite vehicle design in the whole series. :V
That's all the metrics I could think of! I rambled a lot, but less than I was expecting. You have no idea how much more I have to say though. Anyway, in the end, I'm gonna have to go with Head-On Extra Twisted Edition being #1, Black being #2 and 2012 for #3. But Ian, 2 was mentioned a lot! Yeah, I know. Argh. That's one of the things I have more to say on. Here's my overall rankings though.
Head-On > Black > 2012 > 1 > 4 > SB > 2 > 3
There's a lot of things taken into consideration, but gameplay is the most important overall.
I can still go back to 1 and have a great time, even though I do not miss things that did not return, like the human pricks who shoot at you.
I enjoyed 4 more than I thought I would. The gameplay is solid, good soundtrack and I give them props for nuking the entire fucking cast and doing their own. The stages were kinda not the best designed and the bosses sucked though. Super (X) were just lazy and Sweet Tooth was absolute bullshit. The endings also sucked except for like one or two of them. It does have co-op, though be prepared to be playing a slide show.
SB is a bit underrated. Not the best in any category, not the worst either. It was a fun take on the series.
2 being this low is probably going to get someone to send a Bitcoin assassin after me. I love everything about 2 except how the game plays. The cars are slidy as fuck, hitting a wall bounces you like a pinball and the cars are too fast for their own good. I tolerated it as a kid, but as an adult it's just obnoxious.
3 is... 3. Outside of the soundtrack I don't have much good to say about it. x) Primeval is a cool final boss I guess and it's fun to trick him into falling out of the blimp. Uh, yeah, it's certainly a game that exists.
The campaigns are not all equal, but get a few friends together and you'll have a good time with any of them.