Nowadays most men wearing sport shorts and t-shirts at the gym. Women usually wearing sport leggins ( something like that: https://flexyfeli.com/leggings/thematic-patterned ) and tight t-shirts. This style allow to exercise with confidence and ease like you mentioned previosly. Huge reason for choosing your appropriately dress is a weather condition in what you are going to training. Is it warm or cold in the gym? Answer this question and your clothing preferences could definitely changes.
Also appropriate type of clothing depends on what type of exercise you prepare to do. In some cases you don’t need to wear tight clothes at all. Before buying something try to analyse what are you going to do at the gym. There are lots of choises on the market today so you could definitely pick up what you want.
I hope that this short answer could help you and other readers. Good luck!