The classic run (
Thunderbolts by Busiek) holds up IMO. The story-telling leans a little too much on telling vs showing at times, but it does a great job building up the characters and bouncing them off each other.
The big iconic story they're known for is collected across
Thunderbolts Classic Volumes 1 and 2. Those books aren't always in print, so you'll likely be better off buying digitally or second-hand.
The book does continue on past that big initial story, but it's a classical ongoing in the sense that there isn't a clear in-or-out, whereas the first ~12 issues mostly feel like a maxi-series that give you a clear starting point.
After 30 issues or so Busiek hops off the book and Nicieza starts writing it... all the way to issue 109! It's never a bad book, but I think it doesn't really start firing on all cylinders until the later portions of the run. I recommend jumping in with
Avengers/Thunderbolts, reading
New Thunderbolts, and then closing out the run with
Thunderbolts #100-109. I'm not entirely sure if this run is conveniently collected.
After Nicieza's run you get the Warren Ellis run. Frankly I think this run is overrated, and turns the T-Bolts into something of a Suicide Squad knock-off (though it's a not entirely inorganic transition from events at the end of Nicieza's run). It's still got some good Songbird and Moonstone stuff in it, though, and they're the heart of the T-Bolts.
I'm going to detour slightly off to one side and recommend Brian Bendis'
Dark Avengers as the follow-up to Ellis' T-Bolts rather than the actual T-Bolts book at the time. Dark Avengers is a direct sequel to Ellis' T-Bolts starring many of the same characters, but putting them in the same situation as Busiek's Thunderbolts from back in the day (ie trying to pass themselves off as heroes). It's basically Bendis' Thunderbolts book, and it's pretty solid.
Meanwhile in the actual pages of Thunderbolts at the time, you had some fill-ins, and then the brief Andy Diggle run. He had a promising start, but then jumped ship to go write Daredevil or some other dumb book people care about, leading to some more fill-ins.
And then Jeff Parker comes on and starts writing the all-time best T-Bolts. Start from
Thunderbolts #144 "The Boss". He writes all the way to the end of that volume of T-Bolts (
Thunderbolts #174) and then his run, confusingly, concludes in
Dark Avengers #175-190, which resumes the numbering from Thunderbolts.
This is because Marvel started publishing a different Thunderbolts book at that time, starring Red Hulk and a team that was actually
Code Red in all but name. Once again, Dark Avengers is the place to go for your Thunderbolts fix over the actual Thunderbolts book Marvel was publishing at the time.
Red Hulk Thunderbolts, despite not really being a Thunderbolts book, did get pretty good when Charles Soule was writing it, so I do recommend those issues despite it still not being much of a Thunderbolts book. The Soule run is
Thunderbolts vol. 2 #12-26.
Thunderbolts vol. 3, written by Jim Zub, is alright. Zub clearly gets the characters, but unfortunately the art is terrible. A much stronger pick from the last few years is the
King in Black: Thunderbolts miniseries, which is fun, does a good enough job at not getting bogged down in its status as an event tie-in, and is only 3 issues long. I enjoyed it so much I bought the original artwork for one page.
