This article talks a bit about some of the surviving jedi and groups that gathered around them.
Great Jedi Purge/Palpatine's Purge Ranges from 19 BBY to 1BBY. The hunt for jedi who survived Order 66, etc went on the whole time. Obviously closer you get to 1BBY more you are talking about Rebel Alliance or the precursor the Rebellion simply. I vote 12yrs BBY, 15 is only 4yrs since declaration of Empire/Emperor Palp/Vader still kind of new. Few more years gives Empire bit more foundation.
There's also a lot of Darkhorse series in the time period. Individuals and compiled in trade paper backs, The Purge, Darth Vader and Ghost Prison, and a few other Darth Vader oriented series that are all basically tales of him hunting down surviving Jedi and squashing pre-Alliance dissent in the Empire.
I'll have to wait til we spell out the opening event and world subjugation before I finally settle on a character as well.
Am writing up an ornate proposition for that (world event) right now. Will deliver something by late tonite so help the CheeseQuake!
I agree with the SL dynamic Hale mentions, we can publicly hash out character/story ambitions and I know myself am naturally going to gravitate towards something that is a good pairing both against and with others desires. Our starting points in the event will set us with and versus one another I presume.