I don't know if anyone makes a medium size. JP's Corner has men's & women's sizes. http://www.jpscorner.com/coin-cleaning-accessories.html#cotton-gloves Chris
Damage can just as, if not more easily result from a lack of dexterity caused by that gloved hand, and depending on the coin, it is not beyond the realm of possibility that touching, again with that gloved finger, could also cause the value to go down, but surely you know best. If you insist on using gloves, that's fine, but if the coins are worth enough for you to be concerned with handing them, they should also be worth enough for you not to make assumptions or dismiss a well-meaning suggestion, especially being as new as you are, at least without asking yourself why. And you know what they say about making assumptions...
Check at a small independant pharmacy for cosmetic/dermatalogic cotton gloves. I found some for under $5 a few years ago.
The problem with any non-disposable gloves, but especially cloth ones, is that it is like using a pair of socks over and over. Maybe some do, but skin debris, oils, salt crystals, etc , can pass from the skin of your hands to the gloves and if you do not wash them every time ( beware detergents and soaps with chemicals that can change colors) then you are doing more damage possibilities than removing them. Cloth gloves touching the surface of the coin is like rubbing them with a cloth or towel. If you feel you can't handle a coin safely by the edge , use disposable latex or nitrile gloves once and discard. Yes, in the old days dealers and collectors might wear gloves to impress someone that they shouldn't touch it, but they are a hazard. If you drop a coin it doesn't matter much what you were holding it with IMO.
