Thanks.
I built a prototype drawer using a dovetail jig. It took a long time and I wasn't too pleased with my craftsmanship.
I had a stacking dado blade for my construction grade portable table saw and figured with some trial-and-error I could tweak it enough for the rabbet joints.
Glue and brads worked well, and the drawer bottoms added square and strength.
The prototypes were made with plywood, but I found mdf was stable and cut consistently well, and was cheap for the number of drawers I was making. It was heavier, but that didn't matter.
I had a small Craftsman Bench Router Table with a decades old router and it was good enough to round the edges.
I will pick up some better equipment if I start doing more wood-working.