The recreational drives that I have participated in have been very laid back. As long as the harness is safe and correctly fitted, they seem to be happy.
I would not think that you would need an apron or spares kit (though it's never a bad idea to carry some of the essentials with you, like a knife).
My neighbor drivers with a loose check because she says it prevents her horse from eating grass (it's her safety blanket) and no one has ever demanded that she take it off, though we all try to convince her she really doesn't need it.
I usually like to wear a polo and Khakis so I look a little more polished, but most people just come in jeans. I remember when I first went to a recreational drive, I was afraid I would look like I had no idea what I was doing, but I've learned to just relax and have fun, that's the whole purpose anyway! People are usually very helpful and willing to give advice/ answer questions at these sort of things as well. Have fun!