I am one of the few people who currently drive their racecar to the track, for the same reason that makes you consider it: no space (and time to take care of) a truck and trailer.
I got an SSC car, 99 Civic Si, caged. It can be inspected and registered in Maryland where I live, with a few tweaks (needed to reinstall rear belts, stock steering wheel, a basic muffler). These tweaks, and street legality, will vary by state and likely how race car friendly your inspection shop is.
The problem with SS expiring after 12 yrs will hit me end of this season. Yes, most (if not all) SS cars can become IT cars. The problems with this are:
1) A make and model that is competitive in its SS class may not be favorably classed in IT - example is my 99 Si that was one of the cars to have in SSC in its heyday, but is classed ITS in IT, and some people say it will not be very competitive against typical ITS cars (RX7, for example). IF you are considering this avenue, you should ask around what people think is a car that is both good for SS and IT. However, see below.
2) Converting an SS car to a (moderately competitive) IT car costs money - you need, at least, an engine build, full racing suspension, maybe an LSD, usually new wheels & tires, some other minor mods. This will set you back as much or more than it would be to buy a competitive, ready-built IT car - not counting the time and own labor you would invest in an IT build. Quite possibly, these mods could nix your car's street legality. I *am* considering converting my 99 Si into an ITS car, but some people think tht is not a good idea.
3) A SS car with a few years eligibility would obviously be less of a worry, but, frankly, SS has not been doing so well in car numbers recently. I was the only SSC car at a big racing weekend on the east coast. Not sure how well CA is doing - you better check. Possible that SSC is doing worse than SSB. Ask the guys over at the SSC/SSB forums what they think before going SS. There is a possibility that the new BSpec cars may rejuvenate SSC, but people currently wait and see.
Re. the problem of the car possibly not being drivable after a race: Most of my tracks are within 1.5 - 2.5 hrs driving from where I live. I checked how much it would be to rent a U-Haul truck with a dolly or trailer to get the car home, and found that even if I have ot do that once or twice per season, it will be cheaper than all the costs involved in keeping a truck and trailer. Also, I bought AAA premium. For $128 a year, this gives you up to 5 tows per year up to 100 miles to anywhere you want (!), and one up to 200 miles (!). Curious how that will work first time I need it...!
There is a ton of free beginner info on Dave Gran's webpage (SCCA recommends this as novice lecture) including a free senior-racer mentor program: http://www.goaheadtakethewheel.com
You can read about my adventures driving a racecar to the track on our blog: http://www.goaheadtakethewheel.com