20x24 is WAY to small for a nice mat and frame. The STANDARD size for 16x20 is 22x28. It is a standard frame and mat size also. You can buy premade in this size.
I guess one issue would be how much of the paper are you going to cover with mat material. If you are just covering the edges, I think I agree that 20x24 will be too small. If, however, you are going to have an inch or so overlap on each side, I can see how 20x24 would work. When I print, I tend to leave at least an inch of white on each edge of my 16X20s. so a 20X24 works well.
22x28 is standard for many photographers, but many will go abit larger on the 22" side. For my 16x20's, I use a 25x29 frame. It is not so long looking, and gives a nice even boarder on all sides. I usually set the print up 1/2"-1".