OK, rambling response ahead:
You want make music your career... The bad news is that you have to look at the business side of it first, and this is complicated, far more complicated than just figuring out which of three bands to play in. It involves PR, professional associations, work ethic, media law, yadda yadda. And then depending on your flavor of music, you might have to find the time to keep up chops. And after all that there is ZERO guarantee. It's a tough, grueling, sh!tee, sh!tee business. But get an agent, for both work and press; they might be two different people.
Having said this, Band A needs to address the business issues if you want to go anywhere. If they are unwilling, then that's your fun project, period.
Band B, might be a lot of smoke and mirrors. Or not. Tough to know, But I agree with others, the lure of great players is very strong. In their case, however, I might prefer to be on salary for the duration of a tour, and us it for my CV/resume.
I agree with others that band C is a no-brainer, if for no other reason than you control it; you control the business end.
Others have said get promises in writing; very true. And not just that, but it kind of doesn't matter what the bands themselves decide; I'd want to talk with, or at least meet and listen to, whoever is doing the business and what's the plan, and what's concrete. And in the music biz, at least my part of it, probably only 1/4 of what is concrete actually exists and comes to fruition. There are just so many nutjobs in this business it's frightening.
Do studio work, for sure, and if it were me I'd prioritize it. You'll meet more people and get your name around the fastest this way.
I'd be looking at a career long-term, not just in a band. My model for this is Pino Palladino. I don't know him, but looking at his career, one can see a crazy amount of sessions, tours with all kinds of people, and a name that's as big as anyone. And there are others... Lee Sklar, Will Lee, Chris Pratt, these guys have made it in the music biz, and clearly they take the business end of it VERY seriously.
There's a ton of ways to approach your dilemma, and you really should talk with someone face-to-face about what each band offers as an opportunity. This is why you need an agent.
And of course, this is all just my opinion.
Good luck!