Of those, my suggested order of preference would be:

1.) Mesa (obviously, I picked it)
2.) TSA
3.) Republic

Mesa: Quick upgrade time, seems like we're constantly getting more contracts and planes (i.e. sustained upgrades), and the company's outlook is stable and bright, so don't expect to be furloughed or laid off.

TSA: Quick upgrade, I hear almost as fast as Mesa's, but they operate ERJ-145's which aren't long for this world. Trans State Holdings has some Mitsubishi regional jets on order, and while it's possible they could go to one of the other subsidiaries, I hear they're going to TSA, solidifying its ability to continue operating profitably. If anyone else can confirm or deny who's getting those MRJ's, please do.

Republic: Really advise against them. Everyone I know who's worked there hated it. In fact, some of our new-hires quit Republic and came here since their upgrade time is 5-7 years. With staffing problems and labor relation issues, it might not get any quicker, especially if the majors lose confidence in RAH's ability to perform.

That's my humble 2 cents. Hope it's helpful.