This is very important.
The default answer you'll get is a big beefy OS driver of your choice (nukeOS, XXX, FAF firebird, etc.). This is because the OS discs take longer to turn (flip, whatever you call that) and finish, and therefore will get the most possible distance. I don't have a huge OH throw and I prefer a FAF firebird for pure distance. The best I've seen personally is my buddy who throws ~375-400 tommies with his nukeOS.
Now back to the quote. The thing is MANY times I'm throwing OH I don't care about distance, its about hitting a specific shape (usually because I'm off fairway trying to make some magic happen and save 3). For this I want that disc that will fly X feet, then head left....then finish through that next gap. For this reason I throw most of my fairways for OH shots based on how fast I want it to finish. In terms of range from longest to shortest, it goes FAF Firebird, domey firebird, G* thunderbird, (new) stable * teebird, (beat) G* teebird, sidewinder. Depending on where I'm stuck I could be grabbing either of the above to make the shot work.
My best advice is START by practicing with most of your fairways to get a feel for the shapes and distances you are getting and go from there. Once you get the shot dialed in you can do some crazy stuff that makes your buddies curse you out when you save that 3 from horrid locations.
As for your question on thumbers / tommies - in theory there should be no difference (other than R>L vs L>R) assuming your technique is the same. For me, this is incorrect as I can't get as much power on tommies as I can on thumbers so I have to choose different discs for similar shots as a result. No idea why, its just more natural for me. Interestingly enough, my buddy is completely opposite and gets much more power on his tommies (which he attributes to being a pitcher). Your mileage may vary.