Making a wood frame and attaching a piece of acrylic with screws is an option for a door. Getting the door frame assembly rigid enough that it isn't floppy can be a little bit of a challenge, especially if you're just using butt joints (= where the pieces of wood just butts up against the next piece). Make sure you don't screw it down too tightly, as acrylic flexes and expands under temperature and moisture changes and differentials, and can snap if it can't move a little.
If you're thinking about just a plywood box without any additional framing, that isn't necessarily going to work well. Screwing into plywood from the ends does not give a strong connection, especially if the cut isn't all that smooth (not sure how well HD is going to cut down plywood; I doubt they'll use a finish blade). If the 'box' is less than rigid, any movement in it will make the doors not line up. Making a wooden frame and then skinning it in thinner plywood is a better and sometimes cheaper option (since good thick plywood is expensive), but complicates construction.
Not sure what skinks need for ventilation, but that's another enclosure design element to consider.
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