My opinions based on building this. Your skill level and available tools might change the answers I’m suggesting. Also, other readers may feel differently than I do…..
You can cut the dado as you suggested.
You can use a square and a sharp pencil (or knife) in place of a marking gauge.
I’d buy a flush cutting saw - they are not expensive.
A shoulder plane is useful. For some jobs, you can use a sharp chisel instead. Depends on the task. I do like having one in my kit.
I would start small, with inexpensive lumber - handle this as a learning experience (prototype). If you like it, build it again with more expensive material. Or, if you use expensive materials, practice any “hard parts” on inexpensive material first. (You will learn a lot the first time you do a new task.)