Glass is cheaper but heavier. Glass won't warp, Lexan won't break easily. Lexan can be drilled so that hinges can be screwed on. With glass you will have to glue on the hinges. I have yet to find a glue that is 100% acceptable for this purpose. Lexan costs a lot more than glass. Lexan will flex, so if you plan to use a large piece of it on a cage with large snakes, you might want to reconsider. If you are in good with your glass dealer, you may be able to pick up scraps to use. Often they have old pieces of 1/4" plate glass to be thrown away. Forget about cutting tempered glass. It can't be done. If you want to use tempered glass, it will have to be ordered to the exact sizes needed, and will cost considerably more than plate glass. Do you really need tempered glass?
I have used some cheap Plexiglass, and I have been disappointed. I can't remember the brand name, but it had a blue plastic protective covering. I cut the pieces and, before I got them mounted, they had already warped. Some of the pieces were unusable.
Do you want to have sliding or hinged fronts? How big will the pieces be, how much weight is involved? Can you get by with 3/16" or do you need 1/4"?
Lexan seems to be the way to go if you don't want to use glass. You can have it cut, or you can cut it yourself. To cut it yourself you will need a special scribing tool made for the task. The tool is cheap. Some people cut with a saw, but that can leave uneven edges. There is also a special tool made for scraping the dross off the edges of sawed Plexiglass.
For most purposes, I prefer to use glass. It is cheaper, easier to clean, won't warp or get those little "veins" in it.
For many purposes, sliding doors are acceptable and easier. Hinged doors can be easily locked with a hasp or merely by a swivelling piece of wood or metal which will swing over the edge of the glass. Sliding doors require a special lock.
If you are going to use large or very tall pieces of glass, you will probably want to have an aluminum track which will allow for rollers on the bottom of the glass. If you use sliding doors, be sure to have a stop on the outside edges
Sliding glass will also get substrate caught in the track, so build a lip which will bring the bottom of the track above the substrate level, and check the track for substrate. Foreign matter in the track can keep the sliding doors from shutting completely, thus allowing for escape.
There are several grades of plastic track. Use the good stuff. I once made an 8' long cage for some Burmese pythons and used a sliding door system. I used some cheap plastic track, which was all that I could find at the time. I came home one night to find that the burms had pushed hard enough to break the track, and had escaped. They also trashed out some very rare and expensive pieces of ivory and jade while crawling around the room.
If anyone knows of a glue that is 100% effective for gluing hinges to glass, please email me at: firstname.lastname@example.org. I have tried many types, including the two-part epoxy glues. The best I've found so far is, belive it or not, my hot glue gun. I recently used it on a few hinges and it is holding fine.