If I understand your question, almost all cabinets had glass/plexi in front of the monitor. I assume the funtion was to keep people from breaking the expensive monitor by not being able to touch it. Most games also have their Bezel artwork around this glass, so it helps with the decoration value.
As for type of glass - a lot of diffeent opinions. I went with clear glass, 1/4 inch thick. It is very sturdy, you can use it as a table top. Had it custom cut at a glass place, it is about 30"x25" (or so) and cost about $35. Other people go with plexiglass or Lexan. Similar result, maybe a bit cheaper. Some people like the look of a slight tinted glass. A tinted glass will help hide the guts of your cabinet if you don't have a bezel blocking that out. Tinted glass would reduce the brightness/detail of the display, but some people find that more authentic. A good number of arcade games had tinted glass.