the activity will involve running on a treadmill, doing the cylcing classes(spinning), doing body toning classes that involve lifting weights, circuit training.... and maybe use some other gym equipment.........
I have been doing all of these things regularly for 25 years and I have only ever used Reeboks - I have never had any problems. The last pair were around 80 euro I think. I would be surprised if you couldn't get a decent pair of runners from any of the major manufacturers for in or around that price. If not then I don't understand the nature of competition !