I'll preface this with - do whatever makes you happiest. Potentially, you will be living with this cabinet for years. What's most important to you?
For me, my first priority would be to not have to open cabinet doors to get to the drawers.
My next priority would be to have the drawer fronts and door fronts in the same plane.
If just getting the thing done was high on my list, I'd probably go with inset drawers, and overlay doors and be done with it - compromising on my second priority.
If I wasn't in a rush to knock out the project, I'd add 1 1/4" face frame around the outside with 3/4" rails for the bottom two shelves and go with two inset 5 piece doors and inset solid front drawers.