In a previous garage, I used armstrong glue down black and white tiles in a checker board pattern. I then got it professionally polished. My floor was around 35 years old at the time and had a couple worn out coats of red paint and carpet glue on it. The one thing I would do different is to use 4 - 12" x 12" squares of each color to make 2ft x 2ft squares. The 1' x 1' squares I used was s little too busy for me. The tiles were a great solution and I still used it as a garage should be used. Rebuild several cars on it and it would mop clean.
Dave