I doubt that KotOR III would return to Republic space since both Revan and the Exile went to the Unknown Regions to combat, I assume, the "True Sith". So, the game will mostly take place there. We also won't use either Revan or the Exile... what's the point in playing as the same person twice.
In any case, I think the game will revolve on a joint-mission of the companions of both Revan and the Exile to finally find out the fate of their former leaders, and your character being a Padawan of either Brianna or Bastilla, who is of course a prodigy and will become exceptionally powerful during the course of the game. Due to the fact it would be from both groups, the characters I think would be joining the mission would be Carth, Brianna, Bastilla, Atton, HK-47, and Mandalore, they being the most loyal to either Revan and the Exile (or both..) and still being alive (I doubt Bao-Dur is still alive, so I didn't include him).
A new ship would also be in order seeing how the Ebon Hawk is somewhere in the Unknown Regions. So, seeing how Carth would have obvious connections and the fact he is an Admiral, you'd take a Republic warship, possibly the Sojourn since that was Carth's ship during KotOR II. Obviously you would also get the crew of the Sojourn, but they won't do anything besides keeping the ship flying and possibly getting massacred if you get boarded by the Sith, and because we may get an actual warship and not some freighter, the sporatic space battles we got during KotOR II may be more entertaining, but I don't know how they would work.
Anyway, I would assume the opening movie clip will be on either Dantooine or Telos, where the characters I listed before are preparing to leave for the Unknown Regions and are saying farewells to surviving friends and then going off. I wouldn't know what planets they would go to during the journey, seeing how they're unknown and all, however. What I can except they'd find there could possibly be an in-tact Mandalorian colony, for that is where Canderous/Mandalore says the Mandalorians came from anyway (Unknown Regions), the Ssi-Ruuk, some Dark Side planet we have yet to know about, and perhaps locating the Chiss Ascendency, where they would go planet to planet, in which when you gather all the evidence (or whatever..) from the planets it will unlock a new planet which would be the last planet that Revan, the Exile, and T3 would have gone to, where you learn of the fate of both. And provided your LS aligned, they'll join you (not as playable characters, they'll just follow you) and lead you to the planet they have found where the True Sith are, where you will fight and destroy them. Or if you're DS aligned, you'll kill Revan and the Exile (or just find them dead anyway) and go to the True Sith planet anyway in an attempt to take control of them and invade the Republic. Of course other characters would join during all of this, but I'm not going to bother guessing who they would be.