I've found it easier to start with more pressure and then just let more air out later. Takes less time to let air out than go to the pumps and air them up, etc. Doesn't really matter though, whatever works best for you. I would think somewhere in the 16-20psi range would be good though. Maybe 12 psi would work but I would start higher than that and work down if you want to try it.
You can practice launching on the street somewhere with little traffic, etc. But honestly, that won't replicate what the track will be like. At the track, they put down a lot of traction bite stuff (VHT, etc) so your car will hook better there than at the track. Also, typically on test n tune nights they apply less traction bite than on days where they have serious racers there, such as a Sunday with bracket racing, etc. My car hooks great on Sundays at my track, but I had a hard time on Wednesday test n tune last time.
Make sure you bring a helmet, you'll most likely run faster than 13.99. I'm guessing you might be in the 12's at first with poor 60ft times until you get the hang of it and then get into the 11's somewhere, maybe mid/high 11's if everything is right and you hook up good, otherwise low/mid 12's if you can't hook good off the line. There are a couple other guys on here with superchargers on their 5.7L R/T's and they're in the low 12's with 1.8 60ft times and they believe they have more in it still.
The turnoffs are at the end of the track. At my track there are two. I always use the last one, no point in wearing out your brakes. I believe the first one is for slower cars or 1/8 mile cars anyway. If you're on the lane furthest from the turnoff, it's polite to let the other racer turnoff first, even if you're way ahead of him.
For launching, don't worry too much about reaction time if you're just going to make some passes. Just leave when you see the third yellow, that will get you a pretty good reaction time by default. If you wait until you see the green you'll have a bad reaction time guaranteed.
I would just leave it in Drive the first few passes just to get the hang of the whole process. One less thing to think about as you get used to everything. Then shifting with autostick will probably net you the best ET once you get some practice.
The main thing is to just go and make some passes, get some seat time, get the process figured out, talk to some people in the pits and staging lanes as they'll help you out if you tell them you're new to the scene, and just have fun. You'll find it's addicting and you'll want to go back again and try new things out to see how low of an ET you can get. It's a lot of fun!