Like I say, I think it can be a 'school' of sorts, but the chances of recapturing a temple or academy of the Republic or Old Republic is unlikely to happen. I still imagine it becoming a more modern version of the Jedi Order, something more proactive and adapted to the world around it. They simply can't operate the way they used to as the government (First Order) is trying to eradicate them. I think @TheShard 's description of a league is pretty good.
At the same time I don't see why we couldn't also long term try to build up a school on Corellia. Maybe that can be an actual base of operations so people don't go space crazy by being cooped up for so long.
With hindsight we should have done a session 0, and that is at least in part on me.
Reesh as a Findsman does not actively care for the jedi (or really believe he is force sensitive). He hunted force users in the past (which he does sort of feel guilty about) and goes by the philosophy of you are either a hunter or prey, and its your job to choose your side. He currently is looking to stick to to the First Order to ease his conscious (and for a bit of glory towards earning his name), and if joining up with everyone will help him achieve that then he's in. His goals were left open to help him mesh at this stage, I plan to refine them as time goes on depending on what happens, but his long long term thing will be to earn his name and prove himself. worthy of of being essentially a folk-hero by passing the janwuine-jika test. What that entails I couldn't find, but that leaves some creativity to work with.
When it comes to teaching his focus will probably be tracking, hunting and general survival skills. He'd probably impart his philosophy to those interested. He might also show padawans a grittier side of the world through hunting etc, where sometime you have to do things that wouldn't necessarily be light side to be survive, or to do bad to avoid terrible.