Most, but not all pre 90s games were just a plain overlay with no plexi. The plexi came into fashion when operators started installing it themselves because they were tired of ugly, torn up overlays. Of course, the plexi just got ugly and torn up instead, but I guess ops thought it was easier to cut & drill a new piece of plexi every so often than to apply a new overlay sticker.

A cab in your house is probably not going to have cigarettes stubbed out on the cp, or anybody with a Magic Marker or penknife scratching their name into the overlay. If you get a good quality overlay printed, you won't need the extra protection- but that doesn't mean you can't put it on if you like the look.
If you decide you want plexi, the most common alternative is lexan. You'll also hear "acrylic" and "polycarbonate" mentioned- those are just the generic names for Plexiglass and Lexan, which are brand names. (Coke & Pepsi = Soda & Cola)