The best type of clothing for you will depend on what exercise you are doing, what it is for (general fitness, specific event) and how serious you are about continuing with it.
If you want to start jogging, but only in good weather to keep yourself fit, and therefore may stop at any point, you will probably not want to spend a lot of money purchasing all the latest high tech running gear.
However, if you intend to train for a competition such as the marathon or some other sport, and will therefore be training upwards of three times a week, it is important that you do have the correct clothing to ensure peak performance and safety.
For the beginner, you want to choose exercise clothing that is comfortable but practical. The more up to date fabrics such as CoolMax wick the moisture away from your body, so you do not become overheated, cold or clammy. Cotton is fine, but remember that it hold moisture so will become damp and heavy. It is best to choose lightweight cotton.
If you go to classes or the gym, it is up to you whether you want to get kitted up in head to toe lycra, or just a t-shirt and shorts (headbands from the 1980