As for tones, I really like everything from a clipped Telecaster to a Dave Gilmour strat or SRV or a thick Billy Gibbons Les Paul. Without buying them all, I don't know which PRS might cover the most bases but thought it would most likely be a Studio.
Maybe I'm getting too philosophical here, but I'd like to share my thinking, since a lot of my work involves recording my guitar as well as session players who come to my studio,; maybe this will help.
Guitar players often start out by trying to cop their favorite players' tones when instrument shopping. Usually, they have a pretty divergent set of favorites, as you do, and usually they don't have the same equipment on hand that their favorite players used on their favorite records. So a lot of folks simply chase their tails looking for a "do all" guitar when the thing doesn't really exist. Nor can they produce the exact tones their faves make even with the same brand of guitar and amp, for a variety of reasons, some having to do with the recording process, some having to do with the skills and sensitivities of their fave players, and so on.
Any PRS can give you a variety of great tones. And the various models can get "Tele-ish" or "Strat-ish" and the like, but the fact is that they aren't Tele or Strat copies. They're built differently, they have different pickups, different woods, different hardware, different electronics, etc. Same with LPs. These differences in construction, hardware and electronics mean that they will always sound different.
My honest belief is that every player has a different voice. It's ok to play Gilmour compositions on a guitar that is different from Gilmour's. You're not going to fool yourself or anyone else into thinking you sound exactly like Gilmour anyway. So be you.
Find an instrument that appeals to your sense and music making ability and don't worry about covering all the bases, because you can't really do it 100% anyway. If you want flexibility, it's certainly there in the PRS line, and the different models appeal to different people. You're so much better off finding instruments that appeal to your ear and brain and hands.
If you can play like one of the great players you mention, it won't matter which guitar you use to play their songs unless you're in a tribute band.
You don't need to play Yo Yo Ma's cello to be a great cellist or to play his repertoire. In fact, classical musicians try to find an instrument that appeals to their inner voice, and they often spend years looking for something that really fills that bill, and then spend the rest of their lives with it. They don't worry about finding a cello that sounds good for this part of the repertoire or that one. They find something that sounds good, and then they play the repertoire on it (there are musicians who specialize in one or two composers or eras, so that can result in a particular choice, but it's not the usual case).
By all means, find an instrument that makes you happy with its versatility, but don't worry about copping exact tones. That part of the tone chase is an endless fool's errand, as you will see on places like TGP where people go on forever about copping this or that tone, and still can't do it.
Just buy what appeals to your artistic sense, and the rest will fall into place.
You can put your own spin on some great songs, if you allow yourself to be you instead of a pale imitation of someone else.
Note - paradoxically, I sometimes happen on tones that are very close to some of the classic tunes I grew up with, but it's not something I chase, it's usually a happy accident!