Holy Crap this looks amazing!!! I think this looks like it's going to be better than The Force Awakens. Can't wait. Now give me a good third person Star Wars adventure game please.
Forced Unleashed is probably the most recent series of Star Wars adventure games in the realm you're looking for. I never finished them, but they were okay. They were on the last generation of consoles.
The Knights of the Old Republic I and II that were previously mentioned are great games, some of the best from an RPG standpoint and story telling. You could probably get these for PC for cheap, Steam actually had a sale on KOTOR I a few weeks ago.
If you're interested in space sims, you can't do much better than TIE Fighter. It's an older game from the 90s, but it was updated a bit a few years ago to improve the graphics a little and to allow for an integrated DOS Box install for easy setup. You can get it cheap, and it's probably my favorite Star Wars related game ever released. Playing as the Empire gives you a new perspective, and there's something iconic about flying around in a TIE with a joystick...Battlefront was fun for awhile on the current generation, but the space combat is dumbed down and not nearly as immersive as the original TIE Fighter (Plus there's no story line in Battlefront). If you enjoy TIE Fighter, Steam/GOG also have the other space sims like X-Wing, X-Wing vs. TIE Fighter, Rogue Squadron, and X-Wing Alliance in PC formats, all of which have been updated to run on newer systems.