I have nylon dog collars in red, blue and black with plastic clips so I can tell from a distance who is who. My Nigerian dwarf wethers look like miniature deer, so it's hard to tell them apart from my kitchen window. I like to watch them and see who's the "toughest" of the day.
We keep nylon dog harnesses on all of our goats. This gives us an extra "handle" on the goat. We have never had problems with getting stuck on anything, but have had a small issue with a few goats ganging up on a smaller, younger fainting goat and occasionally getting their horns under the harness, but they quickly become unstuck. We use black harnesses because we have white goats, so it shows up more easily from far away.
I only keep collars on a couple of my girls. The majority let me just slip on a temporary collar when I need to but I have couple that, once they catch wind that I'm catching and not just petting, they're out of there!