Nike Frees are running shoes, but they simulate being barefoot, which is something that you want for the gym.
Wrestling shoes are actually already good shoes for the weight room, but if you don't want the ankle support, frees or low cut chucks are a good idea.
I have a pair of Frees which I got off eBay for 65 bucks. The retail is around 85...pretty pricey. Low cut chucks or high cut chucks will run about 25 or 30 bucks. As far as the quality of the Frees, I like em a lot. They are well ventillated, and make me feel as close as i can to barefoot while wearing shoes. But if your weight room allows shoeless, just do that. It's cheap and it feels good. The reason I got frees was because I wanted a shoe that would be just as good for plyos or running/hopping as it would be for squatting or deading. Low cut chucks or nike frees are the way to go, for us lifters who aren't yet yolked and don't need ankle support because we don't squat or dead 31904857345 lbs.