It really depends on the depth that you want to develop your background. I personally would generate at least a subsector, if not a quadrant, and start roughly in the middle of it. (I have a sector generator I've written using a blend of T20, JimV's Alternate method, Malenfant's stellar generation, and my own twists to make it like what I want, so I'd probably go with a full sector build, at least at first.)
Once I had a set of UWPs as a basis, I'd go through and make sure the TLs, populations, etc. match my own personal thoughts. I'd also look for adventure opportunities and travel considerations, like isolated clusters, etc.
I'd then modify UWPs (such as lowering some of the high TLs so that I can develop a logical expansion pattern for my interstellar states), or use what's available. (My app checks for basic reality-shift stuff, such as minimum TLs by atmosphere and starport class, so that's not as much of a worry to me.)
If you need a particular world for some adventure ideas you already know you want to run, drop the world directly into the area you'll be gaming in, filing off serial numbers as you need to.
I'd definitely define in large terms anyway the extent of the various local interstellar polities, and identify the homeworlds of Minor and Major races in the area (my app generates that, as well, so it's easier to see. I can move them around or modify them, of course, as needed.)
While the random UWPs serve as a place to start, I don't feel married to them at all, and am willing to change them as needed to fit my ideals.
Once I have some basic starmaps done, I plot out some basic background identifying the roles of the various classes within interstellar society, so that the characters have a context in which they fit within the milieu.
I make a few notes on adventure opportunities, and insure that I've got easily three different scenarios that are possible to explore within the first few sessions. That way, the game doesn't stall after the first session.
Then I introduce the setting to the players, and find out what kind of characters they want to play. Along the way, you'll end up creating more material, so keep track of that.
Modify the adventures based on the character classes, and make notes on other ideas that present themselves in the process. In time, this may become the basis for a long-running campaign.
Hopefully, this gives you some basic ideas on how to organicly grow a new campaign setting. Yeah, it's detail light at first, but the detail grows as you play, and you aren't locked down too tight, so you've got the room to grow.
Hope this helps,
Flynn