Hey Dean,
I think you are probably good to go with NASA, but check their website. They will accept commerical driving schools for their license requirements but you have to do their HPDE day I think. Might be a limit on the school and applying for their license. Requirements are not extensive with NASA and likely you could attend one of their HPDE/Race weekends, get signed off in group four, and race. I have heard of folks basically schooling on Saturday and racing as a rookie (provisional) on Sunday, don't know if it is true or not, but it seems a little quick.
http://www.nasaproracing.com/images/rules-forms/form_provisional_license.pdf
The SCCA requires you to attend two (or one double) of their weekend schools, and that has good and bad points. It'll take longer, but you do learn a lot as the requirement is 7 hours of track time for a rookie license, on track, in a race car, with other folks. If you go to a SCCA school and get your SCCA license NASA will recognize the SCCA license, but the reverse is not true.
I like the competition level with SCCA and the tech stuff, but I like how NASA is trying to do things differently from the "old school white suit guard" SCCA folks. I'm going to campaign SCCA this year and go to a couple of NASA events to check them out though.
Anyhow to directly answer your question for SCCA you'd need to do the following:
1. Get a SCCA race car. Yep, sounds counter productive to have to have car before the license, but you've got to have a teched, legal, and RELIABLE car for school - you do not want to sorting your car in school, you want to be driving. You could write a book about how to do Step 1 but I'll give you a big hint - Miata. Get your medical forms filled out and handled.
2. Make sure all your gear meets SCCA tech specs, you'll need fire suit, gloves, shoes, helmet and if your suit isn't a three layer you'll need Nomex underwear too. Get a three layer, you'll enjoy it. Expect to spend $1000 to $XXXX on this. I got some decent OMP stuff and spent about $1500 total for everything. If you want to look like your favorite driver expect to multiply that by a large factor.
3. Go to the SCCA website and drill down to the regional level and find out when the school are running. Do a double school, takes about three days, but gets everything done at once in one fell swoop. You'll have about 6-8 hours of class time, 7 hours at a minimum on track, plus time to study, take test, and spend good time with your instructor. YMMV - if you get a bad instructor you'll have a bad time, if you get a good one you'll have a wonderful time and learn a lot. People in the know get good instructors, so having a local racer key you in on things is very helpful.
Sports Car Club of America
One of our fellow IT racers, Dave Gran, wrote a book called Go Ahead Take the Wheel. I've read parts of it and read a lot about his discussion of the book on the Improved Touring forums,
IT.com Forums (Powered by Invision Power Board). His book can be found here and it not only SCCA stuff, it covers road racing and how to get into it.
Go Ahead and Take the Wheel - Guide to Road Racing
I wish I could help you more with NASA but I have not gone through their schools etc. There are a lot of NASA forums though and they are quite active on the West Coast, as fairly active in the SE. Not sure about the midwest.
R