I spent some time deciding what type of joinery I should use. The choices were: bridle joints, half lap joints or mortise & tenon joints.
After weighing the options against each other, mortise and tenons came out on top. I think they will end up looking the best, since the cabinet will not be painted., so these offer the least amount of end grain to be seen. Only the ends of the stiles will have visible end grain, and that will be OK.
After measuring the carcase, I laid out all the joints on the parts for the face frame. I decided to allow myself approximately 1/16" overall, so I wouldn't end up with a face frame that was smaller than the carcase itself.
The tenons were sawed using a hacksaw, and the mortises were chopped out using my 3/8" chisel. It is not a mortising chisel, but if you go slow and don't use the chisel as a crowbar for levering out the wast, it is no problem for me at least - to turn out an acceptable mortise with it.
I really tried to take my time and work accurate, and mysteriously it helped. 6 of the joints were really nice and tight, and only one of them was a bit loose.
When I laid out the joints, I had tried to make sure that all the inaccuracies in thickness would be on the same side, and it went pretty well. The one side is near flat with only a minor deviation in one joint. The other side is not flat, but since it will be the outside, I can level it out after gluing the face frame to the carcase.
With the face frame complete, I could measure directly of it, to make sure that the division between the drawer part and the cabinet part would end up where it should: Behind the middle rail of the frame.
The location for that dado was laid out, and it was then used for determining the location of the other dado. That will eventually house a shelf that will divide the cabinet into two.
My usual method for making dadoes is to clamp down a batten next to the line, and use it to guide the saw. When both sides of the dado has been sawed, I remove the waste with a chisel and follow up with a router plane.
I deliberately made the dadoes a bit narrower than the partitions, so I can make a nice tight fit for them by planing the underside of them a bit thinner, just like I did on the floating panels for the back of the cabinet.
Mock up with the parts.
Mortises and short tenons.
Face frame glued up.
Setup for making a dado.