I would recommend that you not buy anything before you start going to the gym, unless your wardrobe is completely bare. As important as a good exercise habit can be, the gym may not be your thing, and you may find better success with running or a home workout program, or even just swimming.
If you have never been to a gym before, there isn't really any "normal" attire. There are often modesty requirements (not too much exposed flesh/cleavage, don't be outlining the "package" too clearly), but the key requirements are to make sure that you have easy movement in what you wear, and that you have enough layers to transition from "cold" (pre workout) to "hot" (middle of your hardest, most sweat inducing exercise). Wear whatever you have in your closet that meets these requirements (shorts, t-shirt, supportive bra if your anatomy requires one ;-), with sweatshirt/hoody and track pants or other loose long trousers over top) and go to the workout facility.
For many gyms or workout facilities, your first visit is, or can be, a tour of the facilities and explanation of the use of some of the equipment. While you're visiting, check what others are wearing that appeals to you, and use that as the start of your wardrobe criteria. Also, decide what exercise you're going to be doing on a regular basis, as that will make a difference, particularly in the shoes. Running, if you're not going minimalist, is better if you wear a shoe that accounts for your normal foot strike – visit a good quality store with knowledgeable staff that can advise you correctly on the right style of shoe for your gait. I also recommend technical shirts, particularly for runners – these are normally synthetic fibres that wick the sweat away from your skin and reduce chafing. While dry cotton can feel very nice, wet cotton is some of the nastiest stuff to feel on your skin, and can be very annoying, and painful when it chafes.
Bottom line – don't buy too much until you know what you're going to do, and how often you're going to do it. If you work out once or twice per week, and do laundry once per week, you probably only need one outfit. If you exercise 6 days per week, two workouts per day, and try to only do laundry every second or third week, then you're going to need to buy a lot more clothes.