I've done a few cat rescues and my uniform is a pair of heavy leather welder's gloves that come almost to my elbows and a clear plastic full-face shield. A thick beach towel to throw over and wrap the the cat in and a Leatherman to cut any string, wires or fishing line they are tangled in.
Key to avoid damage to either party is to control them quickly by wrapping them in the towel or, failing that, getting the scruff of their neck and forcing their belly to the ground, If you keep a hand firmly gripping their neck to control the head, their front facing away from you, and their belly on the ground they can't bite or scratch. Sounds brutal but the pose they adopt is quite close to the natural position they lay down in.
Most cats seem to resign themselves to the situation if you maintain firm control and don't give them an inch for even a second. You have to maintain an inner peace with being the heavy and completely dominating in this situation. Most people seem to make the mistake of feeling sorry for the cat and loosening their grip. At which time the cat breaks free, spins round, and proceeds to do several thousand dollars worth of unlicensed cosmetic surgery on your face. That full-face shield has saved me at least once. Plastic is your friend.
Sometimes it helps to get a leg on either side and pretty much sit on them. This can allow you to have one hand free to get the towel wrapped around them tightly. But you have to maintain control because in that position your marriage tackle can end up in extreme danger if things go sideways.
Always wrap the beast tightly and completely before trying to cut away and strings or wires. A tightly wrapped and completely pissed off cat wrapped like a papoose also makes a nice gift for someone you don't like very much.