Handwraps are a staple of boxing training. There seems to be as many handwraps for sale as there are ways to wrap your hands. Always buy the ones with the hook and loop closure and Velcro. If you get the ones that have to be tied up at your wrists, you'll always have to get someone to help tie them up for you. That takes away time from your boxing training.
The human hand has 27 bones, and you need to protect all of them. Without hands that are working properly, one can't box. Handwraps should always be worn under bag and sparring gloves, as well as worn when working on the light bags.
There are short handwraps and longer handwraps. Go for the longer ones. They'll offer more protection for your hands.
The easiest way to wrap your hands? Using a long handwrap, put the hook over your thumb. Make sure the tag is facing your skin. It's even better if you have handwraps that have "place this side down" or something similar printed on them. That's the side that goes against your skin.
Wrap it around your wrist three times. Make it snug, but not so tight that it's cutting off circulation. Wrap it around your knuckles three times, then to anchor it, wrapt it once around your wrist.
Wrap it once or twice around your thumb. Wrap it once around your wrist again to anchor it.
From this point on, alternate between wrapping it around your knuckles and your wrist until you have covered your hand. Finish off by wrapping the Velcro closure around your wrist.
I suggest washing handwraps in your bathroom sink. You might want to let them soak in a wash pail or bucket for awhile before washing. I'm glad I did the soaking in water thing the first time I washed a pair of handwraps out. When I checked the water, I found the color had bled. I would have been really angry if I had just thrown my handwraps in with the regular laundry.
What type of hand wraps should you buy? I always suggest buying long ones in order to provide more padding for the hands. Some boxers I know swear by "Mexican" hand wraps, stating that they stick to their hands better. The difference between those and regular hand wraps is, regular hand wraps are mostly made of cotton. "Mexican" hand wraps are often a combination of stretchable cotton and spandex.
There are hand wraps that are marketed towards women. I've seen some advertised as supposedly fitting women's hands better. It's also been suggested to female fighters to buy junior size hand wraps -- those made for kids. But those are usually shorter hand wraps, not enough to really wrap the hands, especially the knuckles, properly.
It doesn't really matter what brand you buy, but it's hard to tell how the wraps will feel against your hands before they're purchased. Can't open up a pack in the sporting goods store, nor tell how they will be from looking at them in a boxing equipment catalog. Experiment with a few brands until you find one that feel good to you.
Pick a good pair of gloves to go over those handwraps.