Between the G11 and S90, is there any difference the type of strobe I would wind up getting?
Not really, but it can. I say not really because the vast majority of modern strobes can be triggered via the camera's internal flash using a fiber optic cable. This setup will work for just about any camera that has been made so that the flash can be "seen" from outside the housing and all the housings that I'm aware of for both the G11 and S90 will accommodate this type of setup.
There are, however, many flashes that can be used via a wired connection to the camera's hot shoe (like the G11 has but the S90 does not). These require an appropriately equipped housing (one with what's called a bulkhead connector and a TTL converter in most cases if you want to use TTL auto exposure), and will end up outside your aforementioned budget: about $600 for the Ikelite housing for the G11 (which comes with a bulkhead and TTL converter, the latter only doing TTL with Ikelite brand strobes) and considerably more for the Fix, 10Bar and others.
Now, even many of these "wired strobes" can be made to work optically via a $100 adapter made my Heinrichs-weikamp. I have one and use an old YS-60 optically triggered through the transparent housing for my Coolpix P5000 and have yet to have a problem with it.
Also, would a strobe used with a P&S be usable later on if I eventually got a DSLR?
I haven't ventured much into DSLR gear, but it seems that more and more housings for the DSLR sector are adopting fiber optic connections for strobe use (this also means making the housings a bit taller to accommodate the pop-up type flashes that they have).
I wouldn't worry about it too much though. The way I see it, if you get an expensive enough strobe that would be worth taking to a DSLR, then you won't have to worry about it working since it more than likely will. OTOH, if you get a smaller less expensive unit more geared towards compact housings, by the time you want to upgrade to a DSLR, you'll want to upgrade the strobe to something more powerful.