You could use strips of wood to rest the shelves on, on the inside front and inside side, because you can't see them. On the visible inside left you could use the supports that fit inside a slot routed on the side of the shelf or use a tongue and grove strip of cherry the same thickness as the shelf. Probably no need for support in the back. Another idea is to put cherry strips along both side walls the same thickness as the shelf and halflapp the strips and shelf so the shelf just drops in.

"Floating" shelves, with no visible supports are typically thicker than 3/4" so that they can conceal their supports. You can't hide much inside of 3/4".

It's challenging to get shelves to fit tightly when captured on three sides like that. You will find that the drywall surfaces are not neatly flat and square;it will be necessary to make a template for each shelf, because they will all be different.

Chris,

Take a look at this sight, may give you a hint or two.

Kats-Scribing shelving

http://www.garymkatz.com/TrimTechniques/scribing_shelving.html

Best of luck with the project, rredogg

You could put strips on both sides of the wall and drop the shelves in. To hide the side strips make the front shelves have an overhang to cover.