Planet Jumping Setting Premise Help

[Varyon]

First off, let me note that, for your campaign, you don't need to actually write up the abilities, you can just fiat that the characters have them (as all the PC's do). That said, if you want to do this as a thought experiment (or think you might later have this stuff apply to individual characters in a different campaign)...

The starting point here should be Jumper. Yes, by default that's supposed to go between dimensions, but the difference between "planet in a different dimension" and "planet in a different solar system" is largely academic, the actual function is largely the same. I believe that has rules for characters with the same power being able to either hitch a ride or follow the target's "jump signature" to reliably go to the same place, so those should work for keeping the party together. Adjust as needed for the way you want it to work. There's not really a mechanic for an ability that can only be used every few sessions (I assume the idea is that the characters will jump to a new planet, stay there for a few sessions, then jump to another), however, so you may have to improvise an appropriate Limitation value there, probably based on Limited Use (1/day is -40%; following the rough pattern from that, where it's +10% per ~doubling of the uses and thus -10% per ~halving, -50% for once every 2 days, -60% for once every 3-4 days, -70% for once every 5-10 days, and -80% for once every 11-20 days).

For the extradimensional entities, I feel those would be fine to handle as an Enemy with a Frequency of Appearance that matches up with when the power will be recharged. Note you do not have to roll for appearance, so long as you have them show up proportionally as often as they should if you were rolling (an Enemy with a Frequency of Appearance of 6 should show up roughly 10% of the time, while one with FoA 9 should show up roughly a third of the time). An additional option would be for there to be escalating strangeness that surrounds the PC's as the Others try to track them down, which would justify them having Weirdness Magnet.

One thing to consider for a campaign like this is the possibility of wildly different cultures on the various planets. Stargate SG-1 handled this by having a genius with Cultural Adaptability, an encyclopedic knowledge of the various ancient Earth cultures, and an exceptional talent for linguistics, in addition to most of the team having high Appearance and Charisma and being genuinely likable people (Teal'c was a partial exception on account of his stoicism, but he was genuinely compassionate and most of the cultures were perfectly comfortable with a no-nonsense stoic; he did run into issues due to being jaffa, however). Stargate Atlantis largely lacked a Daniel-equivalent and their Sam-equivalent wasn't quite as charismatic (and while I'm not good at gauging the appearance of men, I suspect Amanda Tapping had a higher Appearance than David Hewlett), but they made up for it with roughly half the team being Andromeda natives who were already familiar with the bulk of the cultures. The fact that, in both cases, the cultures they interacted with tended to hold warriors in high esteem while they themselves had combat skills in line with Spec Ops certainly didn't hurt them (well, it got them off on a bad footing with the pacifistic cultures, but that's where their social skills had a chance to shine).

So, you're probably going to want most of the characters to be adept at handling a wide range of cultures, probably with one or two capable of working as Face characters (pretty much everyone in the Stargate shows worked as a Face character at some point, but that was largely so the show could focus on a particular character for that episode, switch things up a bit, etc). If Jumpers are integrated as a big part of society, that's likely already part of the training and experiences they go through when working as transporters.

If you do go with the extradimensional beings route, you'll also need to decide if this is something specific to these characters - maybe they harmed such a being's offspring ("No Man has blinded me!") and are now being hunted, or even just cursed to be unable to settle in one place for long - or if it's something that all Jumpers have to deal with. The latter will mean societal effects - the planets will have ways to mitigate the disruptions caused by the extradimensional beings, probably including "encouraging" the Jumpers to go elsewhere as soon as they can.. and they may also face discrimination of some sort, as bringers (or at least harbingers) of woe. The former won't, although it's certainly possible the characters will acquire a Reputation regarding the beings chasing them.