Sal-
Glad to see that you've gotten the bug. I'm a road racer, sometime open track and comp school instructor, and did a few auto-x in the past.
Auto-x is fun because it doesn't require any significant investment or component to go play. 'Run what you brung' and just have fun. No, a cobra won't be competitive unless you chop it up and modify it significantly, but you'll get your three runs in and still drive off to Sunday lunch. In your neck of the woods, SCCA has some events and so do some other groups. Most auto-x events are about $50 or so.
The instruction days are probably where you will have the most fun. An instructor gets in the passenger seat with you and tells you when to push the gas, when to brake, and when to turn. A one or two day event will teach you more about car control than you can imagine. One problem with taking your cobra is that some schools and/or the tracks themselves won't let you go with the standard hoop cages - and instructors aren't usually allowed to ride if you don't have the same hoop protection that the driver has. So if you have a single hoop, you are limited to the schools and tracks that will let you on and have a lead-follow arrangement with an instructor in a car in front of you. You can learn more about the school sessions at
http://www.elams.org/toys/HPD.htm Most schools are about $300-$350 per weekend. One you progress, many of the schools will let you run without an instructor in the more advanced run groups. One thing I do feel strongly about is that no school should ever just put you on track without an instructor for your first time. Way too dangerous. I've been in wrecks with students and I've seen students and instructors seriously injured when things go wrong. There is just no reason to take chances. As an FYI, some of the schools (especially NASA and BMW CCA) count towards a race competition license so that is helpful if you ever go that route. BTW, most car clubs will let you bring your cobra to their schools. Since they want your money, as long as a club car doesn't replace you, you can usually run with BMW, Porsche, Audi, Mazda, and even Ferrari clubs. Just check to see what fits your schedule and track preferences.
Like others have mentioned, you can do some schools like Skip Barber, Bondurant, Panoz, Mid-Ohio School, Jim Russell, etc. These schools have you use their cars - not yours. The instructors also tend to be very good, but they compress so much information into a short period of time that you have trouble absorbing it all. Each school is a bit different, but in general I would say they are good as an experience if you are going to do it one time, but not so useful if you are looking for something to do on a regular basis. Expect $2,000-$3,500 for a 2-3 day session. Nearly all of these are held during the week because the tracks get rented for the races on weekends. Some of these schools have programs that get you your SCCA novice race license. It is a shorter way to get to actually racing, but some get frustrated since they don't teach you enough about how to actually drive and win. NASA, which generally accepts SCCA licenses, has also concluded that the safety stuff isn't as strong and now no longer automatically accepts an SCCA novice permit, especially if that came from one of these schools. They will generally want observe you or do one day of their comp school to make sure that you are safe.
When it comes to racing, you have a lot of options these days as long as your car meets the safety requirements. Vintage racing has very lax licensing requirements, in part because it is a modified wheel to wheel racing environment designed to protect the cars (which helps protect the drivers too). It is still a great thrill. NASA now has their time-trial event which puts you against the guys on track with you to turn a fast lap - not necessarily to be first across the line. SCCA is now rolling out something similar as well. For full-bore racing you can go with any number of groups including EMRA, SCCA, NASA, etc. Most races are about $300/weekend, but some of the Vintage ones can be $750 or so, but that does include dinner. But the real cost isn't the fees - it is the work and prep and spare parts that go into racing. We probably spend about $20K/car in a good year, but in our bad years (engines, wrecks) we've spent multiples of that. I'd probably say that if you really want to try racing, get a cheap spec RX-7 (about $3500) or Miata ($10-12K) or NASA CMC Mustang ($8-10K) and run those cars instead of your Cobra.
Hope that helps a bit! Hope to see you at the track!