I just enrolled at a pro wrestling school, and am going twice a week. Obviously in addition to learning technique, we do quite a bit of conditioning.
To be honest, my conditioning sucks lol, I'm usually completely out of breath pretty quickly. But I imagine it will improve as I continue, and get more comfortable with the technique.
I also just signed up at a gym. I have trained a bit in the past, but not much. I want to start hitting the weights to just get stronger overall.
My hopes aren't to go to the WWE, im doing the wrestling just for fun, but it is my priority now in terms of training. The strength training would be to supplement the wrestling. Would a basic 5x5 program be the way to go for this? With some extra conditioning work or just leave the conditioning for wrestling class? Thank you guys 
Start with a simple 3x5. After a few weeks of training (wrestling) you'll have a better idea of the demands of the sport, how you're handling it and if you can/should add in more strength work or conditioning