You are not overestimating the messiness of it. I don't have a special set of clothes that I wear, but I try to stick with stuff that I can wash easily and is durable. That generally means jeans and then whatever top is weather-appropriate (long sleeved tees in the winter and short-sleeved tees or tanks in the summer). I remember last year I wore a brand new tee-shirt, picked up a cat, and ended up with a hole in it because the cat's claw was caught in the shirt. Try not to wear things that you would be devastated if they were ruined.
Definitely make sure to have a sticky roller in your car or purse. You will end up full of fur and don't want to get too much of it in your car (although it is inevitable that some will end up there). My rescue doesn't have a shelter, but we do have a space with five enclosures for cats waiting for foster, and we let them out of those enclosures to play. I often end up having to get on the floor and pull out a cat who is hiding behind a desk or other piece of furniture, and on those days I am just covered in fur.
I think you'll really like the volunteer work! And if they don't call you back, contact some rescues and ask if they need any help with cats--believe me, someone will definitely want and need you. I think I e-mailed about five rescues when I first wanted to volunteer. Only one got back to me (I'm sure the other four needed me, but sometimes they can be really bad about getting back to people, probably because they are so overwhelmed), and five years later, I'm still with that group.
