I'm reading a book on Chinese history at the moment, so my brain is brimming with the Warring States, the Three Kingdoms, the Northern and Southern Dynasties, and lots of other interesting stuff. Obviously, it's time to think about the Rebellion.
My general approach to "which faction do you support" generally involves "me" (my character) being on or around Capital at the start of the war. A central location allows the kind of choice that isn't available to someone who is stuck out in the boonies. Of course, that's "choice" as in "where are you going to flee to when you escape from Lucan?" rather than a leisurely intellectual decision.
Intellectually, of course, "I" (my character) would presumably be familiar with the track record of the major nobles, so their general political inclinations should be obvious enough. Of course, that doesn't apply to Lucan, who was a non-entity before the Assassination. In fact, most eventual supporters of the other factions probably were willing to give him a chance to begin with, and my character would probably be no exception.
I picked Brzk, of course, because (a) his writeup in Rebellion sourcebook made him look less evil than most of the others, even though he was never going to be Emperior, and (b) he was a comedy talking dog.
I also tend to make the assumption that my character is actually aware of and cares about the details of Imperial politics. I'm not sure that that would be true of most Imperials. It wouldn't necessarily even be true of all Nobles! The implication is, in fact, that "my character" would actually be a Noble in a setting where this kind of choice would be relevant.
For what it's worth, I seldom play military or naval characters, so my characters would, if not noble, largely be spending their time trying not to get drafted or blown up by commerce raiders. In other words, they wouldn't be particularly keen on any faction.
Well, unless they are spies.
Or Ine Givar operatives.
OK, enough of that.
Being your own faction:
Basically, you have to start in a position of some authority, or be able to get into a position of authority in another faction, and then defect.
Assuming the latter case, you really only need to be well-connected. And lucky. After all, you are probably going to be working for Lucan...
The weakest factions of the early Rebellion were probably some of the Vargr groups that started seizing Imperial worlds. While the big players were doubtless real navies, there were probably corsair bands scavenging around the edges, too.
There were probably also pockets of Imperial worlds that came to arrangements with the Vargr, and Aslan, effectively becoming small independent states, at least until someone nastier came along.
Think of it like this: how did Tobia _really_ fall to the Aslan? What do you think the chances are that Tobia and the worlds around it were really a faction of their own, unimpressed by Norris? Yes, I believe there is some canonical stuff about "what happened", but that can be subjected to the "wheels within wheels", "what you see is not exactly what you get" techniques that Traveller encourages.
You might be able to do something in Old Expanses, too. The Solomani takeover might not be quite as tidy as is usually thought. Paying lip-service to the Solomani, while fishing in troubled waters is a perfectly viable hobby, as long as you don't get caught.
And then there are the hi-pop worlds that try to play the factions off against each other.
In other words, there is plenty of scope for subfactions to exist from very early on. Once you get to the Hard Times, of course, the universe is your oyster.