Hi Nick,
Keep in mind that for this application you will definitely want to use either annealed or tempered glass, but the catch is it can't be cut. Once it's tempered, any attempt to cut it with anything other than a carbon dioxide laser will result in a pile of glass shards, so unfortunately your idea for cutting it yourself is right out the window.
This is not a cheap solution by any means, but there's a place near where I live that makes custom tempered glass. You put in the dimensions you want and any edge finishes and/or color options you want, and they give you a price that includes shipping.
I don't know the specifics of the dimensions you need, but I just took a rough number and went through their ordering process for a sheet that's 3/8" thick by 32" wide and 16" deep. I specified one finished edge for the front, and plain clear glass, and the treatment was for annealed glass rather than tempered; the main difference I believe is that annealed glass will shatter into shards and large pieces like you expect glass to, while tempered glass breaks up into small pebbles. The cost with shipping came to about $100, although they do have an option for knocking $30 off the price if I picked it up myself; of course the chances that'll work for you are vanishingly small unless you live somewhere near Vancouver Washington.
[link|https://www.onedayglass.com/|Custom Glass, Glass Cutting & Replacement|new_window=true]
I've used them in the past and their work is fast and excellent quality, but of course you'll have to decide for yourself if that shelf is worth $100 USD or not.