I can't claim to be a full-on expert, but I am a university employee so I have some of this same stuff available to me.
It sounds to me like you don't really have an option re: matching. You're going to contribute the full amount. I have a similar deal -- I contribute a required 3%, the university "matches" 5%.
Between the two, I'd go with Fidelity. Technically, it depends on the expense ratios of the available funds, but my guess is that Fidelity has better offerings. I actually have TIAA-CREF, and they're OK, but not great. Fidelity isn't an option for us.
However, for our voluntary contributions (the 403b), we have more options. I use Vanguard. You could do Fidelity for both, but if Vanguard is available you might want to do that.
Personally, I do the regular 403b as opposed to the Roth because I expect that I'm earning more money now than I will be when I retire. I know that for IRAs, there is a backdoor to a Roth, but I'm not sure if that also works for 403bs. 457b is deferred compensation. My wife and I currently max out our 403bs and traditional IRAs. If we reach a point where we had additional money for retirement, we'd do 457bs. I think they basically work like 403bs, but I've never had one.
After reading the previous posters comments about 457bs, though, I might have to re-think this.