My father was blind, and a little messy, so bought the low priced bath towels hemmed around the top to make a narrow area to go around the neck, were made long so covered most of his lap and used velcro to attach flaps, it worked great, washable and the terry soaked up most of the wet spills before they soaked thru.
Good Luck with you project, what a nice thing to do!!
He didn't want food down the front of his clothes, so had about 10-12 of them could reuse or get a clean one for each meal.

Here's another pattern

http://www.laurassewingstudio.com/NL/060407/060407.html

For 'waterproofing', what about the things that are used in baby cribs to protect the sheets? Maybe they are too thick, but it's just a thought.

My mother used these before she died. Hers were just terry cloth and she had a fresh one for each use. She never had anything go through the bib onto her clothing. Basically the pattern is exactly like a lobster bib. The terry cloth is no more trouble than washing a wash cloth. I made them out of towels so the bibs were nice and thick, not thin like the terry cloth that is for sale in the fabric stores.

I also recommend PUL. If you read diaper instructions, you will understand how to use it. I have to buy it online as I don't know of any independent locals who carry it.

Also what TanyaL and C.Cal said sounds good to me.

I've washed my table clothes several times...you might want to try one and give it a week's worth of washings in a couple days and see if it holds up like you'd like it to.

I worked in a laundry at a nursing home and theirs were just terry cloth It all goes in the wash and very hot dryers.

And the plastic tablecloths etc. that have been suggested .... would melt in the dryer!

Yes I would not use plastic.

Either the heat laminated poly or regular poly, quilted or oil cloth. Make sure to put a crumb catcher pocket at the bottom. Velcro closures are good and easier for them if they are off to the side a little. Great project!