A drag show at a gay club sounds like a great first outing.
Wear dresses if you like, you will fit in perfectly. We went to one before Covid and it was incredible. Best was after the show the performers invited everyone who wished to come on stage with them for a photo.
You should have a great time.

As for the makeover, just tell them where what you want for her look. There is no one-fits-all and they should be happy to make her look her best. I've had a few and they've all been wonderful.