OK
Looks like the leanings are towards M&M Explorers.
... which suggests that in this universe the overwhelming majority of stars have no habitable worlds; there are tens of thousands of stars in a 1000-light-year sphere around earth.
The most recent estimates put 'habitable planets' in the milky way at about half a billion, though 2.5 Billion is also a number that gets talked about a lot. Compare that to the 300 billion stars, and you get a lot of dead space. Even if we were to assume 3 billion, that's still would mean only 1 percent of all stars in the milky way have even a single habitable planet. So yes, an overwhelming majority.
Also, much Sci Fi (And my game in particular) uses planet clusters - lots of habitable planets in an area, followed by patches of empty space and then more clusters. These areas would tend to form stellar nations much like nations on Earth, with 'lakes' or 'oceans' of uninhabited space in between.
AND, keep in mind I said "many civilizations are only weeks or even days apart by FTL." Not that the closest inhabited PLANETS are days apart by FTL (That would mean they were hundreds of light years apart!), but that the distance between civilizations tends to be larger than the distance between planets within a nation... Dead areas of space acting as 'natural barriers' like mountains or rivers on a planet once did.
Beyond that there's also the fact that the vast majority of knowledge has been lost, including 'who is where'. The galaxy is in a re-exploring phase, and it's very easy to overlook a planet when you're hopping around the vastness of space. There are probably many 'lost worlds' no more than a few dozen light years away from some of the more advanced civilizations - they simply haven't been discovered again yet, likely because their tech level is low, or no sentient life survived on them. Or perhaps they want to stay hidden..
I'm favoring M&M and options 1 or 2 myself, perhaps in combinaision? Crash/stranded near the ship, send an ad hoc boarding party to try to solve the problem/scavenge (composed of the most abled present (i.e. the PCs)), ship triggers with just/mostly just the party aboard? Combine 1, 2 and 3? Ship found (embeded in comet?), towed to nearest habitat and put in orbit at what they *thought* was a very safe distance, early activation of some of the ship's functions cause widespread shut-downs (killing some/all of the original science party on board?), ad hoc boarding party sent to try to solve the problem, combined with those stranded in the immediate viscinity (press, police/security, the curious, the ambassador standing by in case this is a first contact), etc?
That's basically just a more specific variant to the 'explorers' option I had proposed.
Re FTL, what about in-system transportation, Jemal? Can it use FTL/Hypers or is there the equivallent of a "not in a gravity well" restriction on the technology?
You've also talked about speed, but what about price? i.e. 2h to get to the nearest system, but at what cost? Do people commute between systems? Work in the outer system by day, go to bed in the heart of the system's capital at night? What about freight? Is it economic to ship base, high-bulk material across systems (metals, frozen gases, food), or is it all low bulk-high value stuff?
Good questions.
First:
Hyperdrive and FTL both have 'minimums' that prevent their usage in-system. FTL travel is only sustainable at a minimum of 1Kc and must be on for at least a few minutes to prevent engine damage. It is not usable within systems for that reason, and in fact most FTL flights end at the outskirts of a system and then use Light-speed engines to travel within the system, to prevent over-shooting.
Hyperdrives are not entirely accurate, so Jumps are also usually planned to hit the outskirts of a system to prevent crashes. It is theoretically possible to plot a jump within a system, or to jump directly to a planets orbit, but even a single digit calculated incorrectly a hundred decimal places down the line could spell disaster.
In system, Light-speed drives are used, capable of travelling up to light speed.
**NOTE: I will be ignoring time dilation from speed, and other problems often associated with 'light speed travel' for simplicity in this universe. **
Within habitable systems(At least the more advanced ones), there are often Space Stations and often more than one planet in a system is habitable (Or may have been terra-formed back in the golden age). Other planets may also be used for resources or to house enclosed colonies, and so inhabited systems can be fairly busy.
Depending on the system, it could take anywhere from an hour to a day to get from a hyper drive/FTL drop-out point to a specific planet, or mere minutes to get between two locations if they're close enough.
Travel within system is common. (Think of each Solar System as the equivalent to a city, or possibly a state/province.)
As far as Price, I don't see that coming up ever for PC's given the nature of the campaign, so haven't detailed it.
Also, though your characters will not know this yet I'll tell you: The ship you'll be on is capable of breaking many rules.. but until its under your control, it does so at my whim.

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I guess in the end we both made VERY different universe, but if you're stealing the basic thing for Stargate: Universe, you're still stealing the same thing.
You'd think if they're that mean of us wanting to steal from it, it would have lasted longer.
I actually don't see that as being a problem. Mine will be very much 'roaming the galaxy' type game wheras I get a different vibe off yours. Also SG:U is only one member of the genre I'm trying to replicate, though I must agree - Why did they have to cancel it? Stupid networks..