When many clients first start training, they are a little unsure of the kind of clothes, trainers they should be wearing. Work-out clothes should be sport-specific to whatever activity you are doing, for example:
Long Distance Running
If you are doing long distance running, you should be wearing running trainers such as Asics that will support your feet, preventing injury to feet, ankles and knees. The best advice would be to get your gait checked. this is a service offered by many running shops who will analyse if you run on the inside of outside of your foot by getting you to walk on a treadmill and offer you training shoes suitable to support you. The trainers sold in this kind of shop may be a little bit more pricey or there may be a charge but it will be worthwhile as you will be buying training shoes that have the right cushioning and support preventing injury further down the line. People tend to hold on to their trainers for 1-2 years, you should ideally replace these trainers every six months if you are using them regularly. They only need to be worn when running/jogging as they are designed for your feet to be propelled forward and would not be suitable for other activities such as aerobics.
You will need a cushioning running shoe but ideally one a little more lightweight than above.
Would require a training shoe that is designed for twisting, stopping and starting, a running shoe would not be suitable in this case and any training shoe should be suitable. You can also buy dance specific shoes which offer more flexibility and offer even greater twisting capability for Zumba/dancing but would not be supportive enough for aerobics.
If you want to do all of the above you could consider a cross trainer shoe. Cross trainers are sturdier than running shoes, offer increased support around the ankle area but this makes them less flexible but do offer a great protection from injury. I would still suggest a pair of running shoes if you are doing long distance running.
There are no hard and fast rules here. I would always suggest ladies to wear a sports specific sport bra for obvious reasons, other than that, any comfortable clothing, it doesn't have to cost a fortune. I prefer to wear cotton clothes to help my body breathe and to keep me as cool as possible. I like to wear leggings and tank tops for Yoga and Pilates but a cotton T-shirt and leggings would also do the trick. You can buy Yoga/Pilates gripping socks in the winter or if you feel uncomfortable with bare feet although this is the preferred option for these actvities.
If you have any questions, please feel free to email me on facebook/twitter or firstname.lastname@example.org.