As for the spinning "Centrifuge" floating in a heavy gas, the axis would be vertical to the gravitational field. It is a possible option, not a necessity. Other methods are well worth considering.
As for Vesta a basalt Terraformer. True enough. However, I speculate on Vesta, only because we have data. I actually think we should look at NEO, and then the equivalant in Martian orbital proximity, and then perhaps something in the main belt smaller than Vesta, and with a clear signature of water being present.
If Phobos and Demos do show to have accessable water, then all the much better for everything. Go there before the main belt.
If Mars is sterile, then surely make something of it. If not, then figure out a plan, try to be moral towards the oganisms. We won't really know the options until we have some degree of certainty of the actual facts. We will not ever know for sure, sooner or later we will have to make a best guess, and live with our decision.
You would be taking a lot of energy out when you decelerate a spacecraft - probably most of it's kinetic energy could be converted to electricity. It's just, you're talking about trying to rendezvous with a narrow strip of metal whilest travelling at 5-10km/s, which is a very hard thing to do...
For launch, though, it would be quite a simple matter. Orbital rings are easiest to build at synchronous orbit, because you can transfer your excess momentum straight to the planet via the space elevators (spokes), though that of course limits your launch velocity to levels that won't kill people through centrifugal force, so about 10km/s max at Ceres. A Terran or Martian ring would have a much greater capability, of course - a Terran one would be able to launch manned craft one a several month trip to Jupiter. But a Terran ring would be harder to construct, for obvious reasons. I don't know how good a Martian ring could be. Perhaps small worlds might be able to manage rings that launch payloads at 3km/s.
An advantage that you've have with using Vesta for your idea, Rob, is that it's very Basaltic. Basalt is a wonderfel material for making fibres with - you could probably automate the entire process. Potentially you could automate the entire manufacturing process for the ring.
Smaller basaltic asteroids might be ideal candidates for such treatment. A lump of basalt a few hundred meters in diameter could be spun into quite the space colony by the crew of a seedship. Maybe several families - or an extended clan - could purchase a ship and go make their own world, maybe half a kilometer in diameter. If it's 200m wide, they'll have about 30 hectares of land on their world. Imagine several thousand of such worldlets spread throughout the belt...
One use of a ring around the small planets would be to accelerate spacecraft electromagnetically. The acheivable velocities would be much higher than those from merely relying on the planets own angular momentum stores. You could launch craft at maybe 10km/s using a ring at Ceressynch without pulping the occupants. Enough to reach Jupiter or Mars in an expedient manner? Perhaps.
Excellent! How thick walls / floors?
... for radiation protection.
Well, you need about 10 tonnes per square meter for the same level of radiation protection that you get from the Terran atmosphere, but we might be able to use electromagnetic fields to cut that down... I'd say that 5m thick walls should be sufficient, especially with a diet that's suited for radiation protection and the amount of hydrogen that's going to be in the ground of the miniworld in the form of water.
I'm thinking of a basalt half-torus ring forming a valley, and some sort of bioplastic (self-repairing) roof forming the inner half of the torus. We're going to need to get a lot of hydrogen into the roof, and make it at least 5m thick... I wonder if we can incorporate UV filters into the roof, so that we don't have to use as much mass? Perhaps, if we use the appropriate materials, we can get the required shielding mass down considerably...
A 1km diameter world wouldn't be able to launch payloads at an appreciable velocity using an accelerator ring, of course - accelerate limits mean they could get to about 250m/s using such a ring. But another, outer accelerator ring... Using a ring 10km out would allow velocities in excess of 1km/s to be achieved, which may be enough to allow viable trade and travel between such ringworldlets if they're only a few million km apart. You could have thousands of polities inhabiting the asteroid belts, trading and interacting without regards to Terra, Mars, Vesta etc...
Put inbred - sorry, *thoroughbred* - clans on these polities, such that they appear to be aliens-with-forehead-ridges to each other, and throw in alliances, betrayal, love, and war between thousands of civilisations, each numbering in the thousands... Probably easier to do this in the Kuiper belt...
Also, much of the design groundwork for such a small ringworld has already been done, it's no different to a stanford torus.
We could build small torus's suitable for a single clan out of asteroids that are only a few hundred meters in diameter, or even less...
Or, around a small asteroid a few dozen meters in radius, scale it down. A ring that's 100m in radius would make a neat little garden world or homestead. It'll have maybe 2.5 hectares of liveable area, made from an asteroid of only 150m diameter. There'll be plenty of those rocks about, and they're much better as inhabited rings than as potential impactors on Terra.
A decent size (20 hectares?) torus would mass far too much to be moveable. You're talking about burning hundreds of thousands of tonnes of fuel to move a habitat at a few hundred meters per second. It's all that shielding that needs to be hauled... that's what drives your mass up into the millions of tonnes. Bear in mind, though, that such a world could be made from an asteroid that's maybe 200m in diameter, of which there's likely to be millions in the belt. They'll be quite close to each other, and if they're say 10 million km away from each other on average, they're going to be a less than a month away (about 20 days) at 5km/s. That's no day trip, but for traders, that should be acceptable, and higher velocities could get it down to a couple of weeks (though that probably means accelerator rings and chemical propulsion for deceleration; the advantage of this is that you have a lot of radiation shielding automatically). At a couple of weeks travel time, you're not stuck to marrying your first cousin Minstrels should be able to manage those sorts of times as well, and help when needed is only 2 weeks away...