Having run it solo and for a one-shot, this is what I've done when running White Star.
I really like Chris Hogan's Thiefless DnD - possibly because bringing in new players was fun with Blades in the Dark. Everyone likes being a thief, it gives them a clear set of goals in a sandboxy game, especially one without some Evil Empire to fight. Stealing shit is also how Conan got started, sneaking into places, all hiding how swole he was until they needed a Plan B. So, everyone is a damn thief. White Star comes with no default thief class, and one can easily be ported, it'll just be better at the thief skills and gain, say, an extra skill point per level.
Having played (and loved) Stars Without Number, a OSR-influenced scifi game with a well-done skill system, it was interesting to come to one with zero skill system built in. Some of the classes just ought to rock at certain tasks (Robots can hack, Pilots can pilot), but sometimes the Mercenary needs to rewire a door or the Alien Mystic needs to use ship scanners. There are plenty of ways to build in skills, but I preferred how Dave Arneson apparently handled skill checks. Have the PCs roll 1-5 d6 and compare it to their relevant stat, plus half their level, _if_ their experience ought to help them. This way the stats don't have to get upgraded every time the PC levels up, but you also get to say that the characters get better at certain things thanks to their experience.
So that is every non-combat check covered, as far as I'm concerned. Either the PC can Just Do Stuff, or its looking for hidden doors or hiding in shadows, or it's something related to Int or Dex or whatever stat. Obviously it's OSR stuff, so if the player is banging every floor tile with a 3.048 meter carbon-fiber stick, they'll find the pressure sensitive traps or illusionary floors without any roll. But I like having some arbitrate system when things aren't that clear.
Speaking of Kevin Crawford's stuff, in addition to using some sector generating rules and some faction stuff from Stars Without Number, I've been using the add-on rules for Stellar Heroes to make one PC games work. It was for a one-shot, and allowed the PC to get through that entire built-in scenario without too much difficulty. The rules may be a bit on the cinematic action-hero side of things, but I can attest that it's easy for the PC to take on too much very quickly. Death can still come swiftly - as it should in these games, especially at low level.
(At the same time, one character in a Fighter-type class, with decent gear and tactics, can take out small squads of opponents. I'd imagine that becoming a plot point - surely military leaders would notice super soldiers in their backyards. It might be a little too on the nose, but I imagine it could lead to some interesting sessions. Militaries might want to hire the PC, or vivisect her to find what makes her simply better than anyone else. It's like Emily Blunt's character from Edge of Tomorrow.)
When running solo, I used Scarlet Heroes, and had fun with the dungeon and urban adventures it can generate. It's not for everyone, but it's a great way to learn a system or experiment with adding on random blogpost stuff, without having to corral players into a game that may or may not suck.
I also ran some Stars Without Number games solo, using Scarlet Heroes, but it's not a system that requires any customization. It's very good as well, I just wish it had a built-in 'Jedi Knight' class like White Star. There's also something awesome about creating your own brew of the White Box game.
It's not something people are clamoring for, but I am going to work out a way to play Dungeon Crawl Classics' funnel adventure solo. That system is too awesome, and it's been sitting on my shelf too long. I'll run through Frozen in Time and see how it goes, so I can see how that scenario can play out for actual, live humans this coming Thursday.