Here is the list of tools I've used to build my cabinet.
Jig saw
Screw gun/cordless drill
Circular saw
Router/table
Sander
Drill press
Table saw
Miter box
They are listed in order of importance. I would saw that FOR SURE you need the first three, and the 4th if you're doing t-molding.
Jig saw: I don't know how you'd cut curved contours on cabinet sides without it.
Screw gun/cordless drill: You need something to poke holes for buttons in your control panel. In addition, at least my cabinet has a pile of screws in it. You could do it with a corded drill, but much easier to get in tight spaces with cordless.
Circular saw: About the only way to get straight cuts for panels. You could try it with a jig saw I suppose, but I have never been able to cut a straight enough line for cabinet work with one.
Router: Only used it for t-molding and undercutting my CP for my joystick, but you can't do either without a router.
Sander: If you want a nice finish on your paint/wood, you'll need a sander I suppose you could do it with a cork block and sandpaper, but SLOW...
Drill press: You can punch 1 1/8" holes with a handheld drill, but it's MUCH easier with a drill press.
Table saw: I have some internal support wood blocks that connect two non-perpendicular surfaces. I ripped 1x1 dowels to match the angles. You pretty much need a table saw for that, but I think you could probably build a cabinet without angled blocking.
Miter box: Just easier for cutting off internal blocking, but wholly unnecessary.
My brands are Skil for the jig saw and circular saw, Dewalt for my 1/4 sheet palm sander and screw gun, Craftsman router and table saw, and Delta miter box. None of it high end stuff, all of it I've owned for 10+ years and has been used on a variety of projects. You won't regret buying any of it...