It starts with just the wraps themselves. There are two basic kinds of wraps for training, those that stretch and those that don’t. I first got a set of Mexican (stretchy) boxing wraps about five years ago when a friend from America came to visit. I had never seen that style before but these days you get wraps in that style from Thailand as well as most of the European and American manufacturers. The other style of wraps (like my older Twins wraps from eight years ago) don’t stretch, at all. Wraps also come in several different lengths, from 4.5m (180 inches) down to 2.75m (108 inches).
The advantages and disadvantages of each style and length are different, and as long as the wrap is doing its job of protecting and supporting your hands, it doesn’t actually matter. There is no right or wrong outside of the primary purpose of wrapping, as long as they are protecting your hands it really doesn’t matter if they are pink Hello Kitty stretchy wraps or non-stretch black and gold ones with dragons all over them. It doesn’t matter. As long as they’re doing their job, it’s all just personal preference.
Another thing to consider is hygiene. If you own your own gloves then it’s not such a big issue, at worst your gloves will smell a bit sweaty and that’s not the end of the world. If you wear club (shared) gloves then that’s a different matter. Your wraps help absorb sweat and help to prevent any infectants that are on the lining of the glove being transferred to your skin.