bumpfich,
The TSA business is far less painful than you might imagine. You might as well register on the TSA website and do as much as you can now (the first step involves the information that you mention) and get it out of the way; the only hassle is that you'll need to scan or fax your passport and visa. Once the first step is out of the way, it all runs quickly and smoothly.
Since you're going to Naples, I can let you know my experience there: everyone is flexible and accommodating with the TSA arrangements there, so it won't hold up your training at all. In particular, the local deputy sheriff who does the fingerprinting (for free I might add) is a nice bloke. So don't worry, get out there and do your flying!!!!
Cheerio, dpm