What kind of 3/4 wood do you have available at your local stores?
I have used white pine and regular birch plywood for shop drawers. For the kitchen, I used poplar and maple planed to 5/8 inch. I don't like the look of 1/2 inch and I didn't want 3/4 inch, so 5/8 it is.
The drawers in my workbench are simple 3/4 inch pine with 1/4 inch bottoms. Simple butt joints, glue and brad nails. They get opened and closed many times every day. Two of them are full of clamps.
Just remember that 1/4 inch plywood is not 1/4 inch. If you cut a 1/4 inch groove, the bottom will be loose.
That's my story and I'm stickin' to it!