Double check all your work before starting up. Prime the oil system, fresh battery, no forgotten tools in the engine bay, fresh 91 (or 93) octane, etc. Turn key to the ON position and listen for the fuel pump to prime, get out and check for leaks. At this point the car should be OK to be fired up and let idle. I'd stay out of boost. A lot of people will drive their cars to the tuner. At least this way if you have any small issues (self inflicted) you can get them sorted out at home instead of paying someone else to do it for you. At any moment you feel like something is wrong then turn it off.
I have a stock 5.0 and I supercharged it a year ago over last winter. I was nervous AF on my first start up! With lots of new fuel parts, PiMP ECU, and the blower I was afraid something would go wrong (like being too lean or rich). What do you know, car started up and idled very well the first time! Tuning it was a lot of fun too.
One more thing. If you have free towing coverage then you could use it to get your Mustang towed to the performance shop. I've done this before but I don't tell the insurance company that I've modified the car and getting it towed in order to get it tuned.