Kurt:
I use something like this
http://www.officedepot.com/a/products/274457/Office-Depot-Brand-Slanted-Sign-Holder/. They're cheap and effective and keep the mud and water out of your face. I put up a clear shower curtain cut off for length on the back part of the desk where I carve to keep the mud off my bookshelf which is at the back of my desk. The mud wipes off with a damp sponge, and since my desk has a formica top, it too, is easy to clean. The extra shower curtain has come in handy for making covers for other pieces of equipment.
When I'm really going to make a mess, I use larger sheets of plexiglass and clamp them to what ever's handy; desk, table, etc.
Some guy was teaching stone carving at my local club a number of years ago and constructed plexiglass cubes with holes on the sides for you hands and flexshaft, and a tube going in the top for a water drip. I think he spent more time teaching how to make the cube than how to carve, a ridiculous waste of time and money. It looked like it would have been horribly uncomfortable to try to work in, and difficult to clean and be able to see what you are doing. Needless to say, he had very few students. Who would want to spend all that time making that box when they're not even sure that they like carving?
Ordinarily, I don't have that much water splashing around that it's an issue. I usually just dip my stone in a bowl of water and when it starts looking dry, dip again. When I do the rough shaping it does get a bit messy, but after that, not so much.
A friend of mine had a "real" point carver from Idar-Oberstein, and I seem to remember that it was open with no water shield. The point carver that Foredom makes doesn't have on either.
Just my opinion. I'm like you, Kurt; entirely self-taught. But you and I have been doing this for years and years and have learned a lot along the way.
Debbie K