I have used these and cotton gloves as well when handling my MS Morgans and other MS/PF coins. Only thing I can add would be to get a jeweler's mat or something similar for the table to protect against rim dents should you drop the coin. Gloves provide protection but can sometimes limit dexterity and "feel".
If you're the type to use gloves - I'm not - nitrile is fine. It's more about a decent fit which doesn't surrender manual dexterity and tactile sensation than anything else, which is one reason I'm no fan of cotton gloves.
Dave, I do agree the cotton gloves are a bit thick. And the reeded edge on proof coins can snag. BUT, they breathe better than the nitrile gloves do. I may switch over once I use up the cottons I have now as they WOULD be better dexterity wise. And I can pretend I am on the ambulance again. ;) LOL