halcyon iris
This is all dry fit at the moment. I'm looking to make a door and a drawer on the front of this. What would be the simplest way to do that? I have plenty of wood to do stiles and rails. I'm thinking of just a single rail for the drawer and then an inset door. If so, what hinges and drawer slides (soft close) do I get?
gilded light
An inset drawer and door are not the simplest way to add drawers and door - assuming you care about getting your reveals even. Partial overlay would be the "easy" way to go. I do like a nice inset door though.
As for what hinges and drawer slides? There's probably some soft close options that aren't European hinges but I'm not familiar with them. I'm pretty sure there are European style hinges that would screw into those stiles.
Blum and Rockler both make soft close undermount soft-close drawer slides that might work for you. They both look good and I believe they have the extra hardware to mount on a frame and panel cabinet side.
It's a little hard to see how thick your back and sides are. You might need to put some extra wood in there to support the slides on if it's 1/4" plywood.
To be honest, I usually have hardware figured out well before I get to this stage of construction and have already accounted for how it's going to be mounted. I'm probably not the best resource for retrofitting hardware into projects.