I would like to put my 3 ft x 1 ft x 2 ft shelves on wheels. They will be used to hold books in my classroom so they need to be fairly sturdy. However the wood is only 3/4 in thick. What kind of wheels should I use?
Bookshelves are not designed to be trolleys!
They will tear themselves apart if casters are put on the corners.
I would have a 1" plywood deck to be a "chassis" that carries the dynamic forces between the casters. Fasten the casters to the plywood deck, then fasten the deck to the bookshelf. Normal wood bookshelves are not meant to roll around, and do not have the physical strength needed to sustain the dynamic forces of being rolled around.
If you've ever pushed a cart on casters, and had it jump or stop abruptly when it hits a low spot, doorway threshold, pebble or pavement crack -- then you have met the dynamic forces I mention. Your generic IKEA tier plywood/engineered-wood bookshelf just can't handle that.
For that matter, you may have a problems with books blowing through the thin back sheet on most bookshelves. You might replace that with 1/4" luaun plywood and lots of wood screws, and predrill them especially if they're going into engineered wood or particle board.
Casterwise, you want the smallest wheels possible. The problem is, larger wheels mean the center of the wheel is farther inset from the edge, and that means the actual footprint of the wheels is getting smaller and smaller. 1" wheels = 11x23" footprint. 4" wheels = 8"x20" footprint. 8" wheels = 4"x16" footprint. Too small a footprint makes the bookshelf increasingly "tipsy" when being transported, so instead of stubbing its toe, the bookshelf may fall over.
Books are heavy, so heavy-duty casters are what you need. You will need a set of 4. Typically you get two with brakes and two without brakes so that you can easily lock it in position (especially important with kids). Something like this:
plus you will need a bunch of wood screws - heads larger than the holes, as long as possible up to the actual thickness of the wood. You may want to add additional wood to the corners in order to be able to use longer screws.
Consider whether a ready-made furniture dolly might fit the footprint you need. If the dollies you find are too large, choose one constructed in such a way that it could be disassembled, cut to size, and re-assembled. Think of it as a parts kit. It's often the case that a set of four casters costs about the same as an assembled dolly. The shelf could be reinforced and attached to the dolly as recommended in Harper's answer.