Infodump: What would have happened had you gone to other universes?
One of the most asked questions is about other universes and what the storyline would have been like had you gone elsewhere. To answer that, here are some of the highlights of what would have happened:
Star Trek
NOOB Mode. Very sandbox-y with no real threat to the Imperium but the Q, and even then the Q are mostly content to watch things play out. End game would have been leading a crusade back into the home universe, at which point there would have been the resurgent Necron empire that dominates physical space after cutting off the Warp from real-space and annihilating the Tyranids. The other half of the Materium battle would be against a resurgent Ork species that rediscovered their Krork ancestry once the Necrons became resurgent. These Krork would have been nothing like Gorehowl, only wanting the destruction of all thing non-Orky due to their genetic memory/intelligence being corrupted. Lastly, you would have to fight the 4 Chaos gods and their minions in the Warp and on Daemon worlds, who have been biding their time against the Necrons, waiting until they are dealt with one way or another before coming back in the galaxy to take it over.
Star Wars
Easy difficulty. You would have arrived during the end of the Clone Wars and have the option of allying with the nascent Rebellion or Empire. There are advantages of taking either route, and the end game here is to unite the Galaxy and launch a crusade back to the home universe. See Star Trek for what that would entail.
Halo
Easy-Medium difficulty. You would enter into the Halo-verse just after humanity loses Reach to the Covenant. It would be an uphill battle to unite humanity under the Imperial banner since they already have Unified Earth Government leading them against the Covenant, but if you manage to do it you would be able to turn the tide in the war against the Covenant. Then you'd discover the first Halo installation, as well as the fact that the Gravemind could be considered a Daemon Prince. It'll roll from there to basically the same as in Halo canon, but with added Imperial support. The difficulty here is that you would have no time to build up infrastructure. You would need to join the fight against the Covenant, who are barely below tech parity with you, with only your current assets and have little time to build up more. Once the Covenant and Flood are dealt with one way or another, you'd rebuild and then lead a crusade back into the home universe. See Star Trek for what that would entail.
Sword of the Stars
Medium difficulty. You'd arrive at the height of the various empires, on the cusp of the Lords of Winter's arrival. That means that there's still plenty of space up for grabs, though territory has been well established for a good while now, and the true threat is just about to hit. Speaking of threats, you would be above tech parity compared to the lesser races, but the Lords of Winter will be far and beyond even DAOT tech. They would also possess insane psychic power, with each Lord being in the range of a Daemon Prince in potency. Thankfully, it will be relatively easy to unite at least some of the factions against the threat posed by the Winter Lords and their Zuul slaves. Once the galaxy has been pacified you would have the option of leading a crusade back into the home universe. See Star Trek for what that would entail.
Galactic Civilizations
Medium difficulty. You would be entering the universe over a shielded Earth as the prophesied crusade fleet. The Thalan would be very hateful of you to start with but you have the option of attempting to diplomance them to your side to fight against the Drengin empire. Speaking of the Drengin, they have greater tech than the Imperium as of the Exodus. The Gal Civ universe is pretty much DAOT and Pre-Fall Eldar levels of tech but severely lacking in psyker resistance so Warp shenanigans would have been what saved you early on. Mid game would have been reclaiming the human colonies and liberating the galaxy while end game would have been leading a crusade fleet back into the home universe. See Star Trek for what that would entail.
Mass Effect
Medium-Hard difficulty. You would have arrive just as humanity discovered the Mars Archives and have been able to unite and lead mankind out into the greater galaxy. Council/Terminus races would be far below tech parity, but from there you would have realized that your Warp Drives are completely fucked until you found a way to greatly amp up your Geller Fields. Oh and the Reapers? You would have also found out about the Reapers (as well as the Reapers find out about you) the first time you try using your Warp Drives. They're actually daemons possessing massive bio-mechanical constructs and propagate themselves by harvesting souls to create new daemons to possess massive bio-mechanical constructs. As for the star-child? A Warp God. Not necessarily malevolent, but definitely antagonistic. And then you'd realize that the Star Child was working to prevent actual Chaos Gods from spawning, which your coming would have led to. So End Game in ME is fighting just birthed ME-verse Khorne, Tzeentch, and/or Nurgle depending on how well/badly you did against the Reapers. Of course, you then have the option of rebuilding and launching a crusade to retake the home universe. See Star Trek for what that would entail.
Endless Space
Hard difficulty. You would appear over Auriga during the time of Endless Legend. You'd have the option of interfering with the various wars and politicking down below while trying to find a way out of the Auriga system's Dyson Sphere. Once you find your way out, you'd have to confront the rest of the galaxy at the height of their power, as well as deal with a resurgent and corrupted Endless on top of an extremely hostile Harmony empire that took over more than 3/4 of the galaxy due to having very non-specific needs in what planets they colonize. While warring against the Harmony and Endless, the Cravers would achieve apotheosis and create a the Endless Universe version of Khorne, Slaanesh, and/or Tzeentch depending on how well you do against the Harmony. End game would have been sieging and then invading the Craver homeworld, which has turned into a mini-Eye of Terror and Daemon world, and then fighting the Gods. Of course, you then have the option of rebuilding and launching a crusade to retake the home universe. See Star Trek for what that would entail.
Sins of a Solar Empire
Very Hard difficulty. That thing that the Vasari remnant are running from? An insane Chaos/Tyranid hybrid abomination. If you follow Sage of Eye's CORE, then think more intelligent spacefaring Chimera with a Chaos God for a Queen.
You would have entered the battlefield about 6 months before the "Darkness" catches up to the Vasari, but you'd have approximate tech parity with all factions and would be in a good position to unite the ailing TEC under the Imperial banner due to Imperial psykers having no answer among the Vasari and Advent. Mid game would have been a mix of diplomacy and intrigue against the Advent and Vasari loyalists and rebels, and depending on your choices you could either annihilate one or both factions, or unite one or both factions under the Imperial banner. End game would have been fighting the Chaos/Tyranid hybrid and destroying their Queen in this universe's just formed Eye of Terror. Of course, you then have the option of rebuilding and launching a crusade to retake the home universe. See Star Trek for what that would entail.
EVE
Extreme difficulty. You would have arrived in modern day EVE, with all that entails. You would be severely out-gunned, out-teched, out-manned, and out of luck. The only way to survive is to take to null-sec space and forge an empire out beyond the reach of the 5 empires. However, the capsuleers have much longer reach than the empires and so you'd have many encounters, both friendly and hostile, with them, assuming an independent capsuleer faction doesn't want the resources you're going after, of course. While you mostly have ground superiority, they rule space and it'll be an uphill struggle for you to carve out an empire and rule among the other 5. It'll have been even harder still to unite the galaxy under your banner and then deal with the various inter-factional politicking. Of course, should you actually unite Eve, you'd find that the wormhole in the center of the galaxy that was lying dormant leads to the center of the Eye of Terror, allowing you to easily launch a crusade back to your home universe. See Star Trek for what that would entail.
And lastly, we have Starcraft. While I won't get much into specifics here since I'll be going over what would have happened in a separate infodump, I will say that SC was Medium difficulty.