I want to say IMO, one should not use 'plate glass' on an arcade cabinet.
If plate glass breaks, its razor sharp shards can cause serious or fatal injuries. Its also quite weak, so breaking it is quite likely to happen, if kids are messing around...
Tempered glass is what you would want in that application. Tempered glass is very strong, anywhere except the edges. You can hit it with a sledge hammer in the middle.. and it wont break. This would have to be ordered to size, as I do not believe you can cut it after the temper. If tempered glass does break.. it does so in uniform sized, small pieces, that are really dull to the touch.
As for reflectivity, there are coatings that can be applied.. same as I have on my eye glasses. Probably not cheap however. A lot of the elder games used a polarized / tinted plastic plate that sat behind the monitor glass, right on top of the monitor surround bezzle.
You also may find specialty films you can apply to glass/plexi for external light scattering. Many Laptop screens probably use this, or a similar spray based coating.