Start with a "Work Mate" -- a folding workbench that also clamps the work. Add the optional clamp accessories.
A good 8" circular power saw.
One fine carbide tooth blade
One carbide tooth combination blade
A cordless drill and good set of drill bits
A 1/2" corded drill for heavier work.
From there, it depends on the kind of work you plan to do.
A Router with some basic bits lets you do some fancy work.
I wouldn't want to be without my HD jig saw
A lighter duty scroll saw is pretty handy
Interestingly you asked only about power tools but the most useful tools around my house are not powered.
24" crosscut hand saw
24" carpenter's square
1" x 25" tape measure
a chaulk line
Set of wood chisels 1/4" to 1"
Set of cold chisels
Good set of about a dozen screw drivers with big handles NOT those darned multi-blade things
Small, medium and large needle nosed pliers
Medium and large channel lock pliers
Straight and curved jaw Visegrip pliers
Medium-sized slip-lock pliers
S, M, Lg. forceps
Heavy Duty utility knife
Left curve and straight compound cutters
Sturdy, fine-tooth back saw
Wire stripper (the small, cheap kind works best)
16 oz. curved claw hammer
16 oz. ballpean hammer
A vise or other holding device
Several pairs of C clamps
6", 10" and 12" "crescent" wrenches
10" or 12" Lineman pliers
Barb-wire fencing tool (great for holding, bending, cutting and twisting wire, putting in tacks, pulling staples,)
6" and 10" flat pry-bars
I could go on but one tip: when you have a job to do and don't have the right tool, don't improvise; go out and buy the right tool. In that way you build up an inventory of tools to tackle most any project.
Loved tools since I was a little girl in my grandads carpentry shop