The above posts are far too huge for me to quote, so here's how I see it going:
The Exchange goes on, business as usual. The power vacuum left in Goto's faction of the syndicate is filled by another crime lord quickly and without much fuss. I imagine that the Exchange will eventually either be usurped by Black Sun, or turn into Black Sun itself.
The Mandalorian clans somehow manage to grow, but implode and scatter for some reason after their numbers climb above negligible levels. The most probable cause is the disappearance of Canderous Ordo after Malachor V's destruction; they carry on for a while without him, but don't last for long, especially since he took the Mandalore's helmet with him. Much later, a Mandalorian on Geonosis (?) would be recruited by the "True" Sith to re-unite the clans and help them against the Republic in the "Great Galactic War". Hell knows where or how the Mandalorians got their fleets and gear, not to mention the industrial centers necessary for such a buildup... Maybe the Sith just gave them a fleet?
By an unknown means, the HK-50 factory is shut down and/or destroyed after HK-47 departs from there. The HK-50s are eventually purged from the Republic fleet, since the Exile knows their true purpose, and the production of HK droids is ended for good. HK-47 himself is somehow marooned on the planet Mustafar, where he remains (ostensibly trying to build a droid army to take over the galaxy with, like that's possible
) for several thousand years until he is destroyed by a group of spacers during the Galactic Civil War.
The Jedi Order will get up and running again soon enough. As Darth Traya implied, the Exile's Force-sensitive companions start rebuilding the Jedi Order, probably by scouring the galaxy for willing Force-sensitives or surviving Jedi to train (I imagine that, considering how dangerously low their numbers are, the age requirements of Jedi recruits would be abolished for the time being). "Disciple" Mical becomes a member of the hastily-formed Jedi "Council". After a number of years of rounding up Force-sensitives, Revan and the Exile's companions band together, except for Mical, who is left to watch over the new apprentices, and head into the Unknown Regions, where they meet their deaths alongside Revan and the Exile, having failed to do anything more than stall the Sith invasion (exactly how they could do this, I really don't know).
While his former colleagues are off getting themselves killed in the Unknown Regions, Mical continues to guide the Order, and eventually a proper Jedi Council is established, lost Holocrons and artifacts are discovered, the Jedi Temple on Coruscant is reclaimed, and so on. Also, because of the disappearances of Visas, Atton, and Revan, the Exile, and their other companions (most of whom have very questionable views on the Force and morality in general), the Jedi Order's fundamental guidelines and doctrines (no use of the dark side, serve the Force instead of the government, marriage is a bad idea) remain intact. As the Order grows and gets its public relations fixed up, a new minor Sith threat pops up every now and again, consisting usually of a small Sith fleet not much larger than a sector fleet led by a survivor from the Sith Triumvirate or some such thing, but these threats-of-the-week never last long.
The regicide it suffered in the final year of the First Jedi Purge, combined with the destruction of its most critical non-industrial planet (I have no idea why Avellone thought it realistic that the entire Sith Order was literally striking from one star system) effectively destroyed the Sith Triumvirate's holdings in the galaxy, and it killed itself very quickly. Those that survived its last civil war were finished off by the recovering Republic's military and the Jedi Order. Obviously, no survivors or successors of the Sith Triumvirate lived to see the "Great Galactic War".
The Republic itself, now no longer being pestered by the Sith, is able to focus on rebuilding, now that it is no longer challenged by any notable military threats. Within three centuries, its respectable military is rebuilt, and the Senate starts anew, with fresh faces overturning what corruption may have taken root since the Mandalorian Wars.
Sadly, most of this is undone by a deadly retardation virus that spread throughout the galaxy, preventing the Republic and Jedi from realizing how stupid it would be to agree to a peace treaty with the "True" Sith after they invade. By the time the virus wears off, it is too late, and they're in the middle of a cold war with the Sith, and both Republic and Jedi public relations have been shot to hell again.
Somehow, however, the Sith Empire is ousted, the Jedi return to Coruscant, public relations are fixed again
, and the Jedi and Republic fortify and rebuild themselves again
for 1,600 years until the New Sith Wars.
As far as I can tell, that all meshes pretty well with canon, for the most part.