I use round, half round and rectangular rasps. A small block plane, a spokeshave.
80, 180, 220 and 400 grit sandpaper (dry sanding). Finer grits 600 up to 1500 or 2000 if you want (for wetsanding finish coats). I cut my initial neck angles (top and both sides) with a Skilsaw, nyuknyuk, and borrowed the use of a big belt sander to plane them flat. Rasps, plane and spokeshave for the initial shaping of curves, then sand til it feels nice....oooooooh yeah!
Jigsaw is handy for cutting curved body shapes. If you build the body by sandwich glueing 3/4" plank together then you can jigsaw cavities beforehand. Definitely need a drill and a large assortment of bits. Even some oddballs. Grover tuners required 25/64" drillbit which isn't part of the average set. Had to buy it separate.
Router makes some of the hardest areas quick and dirty...and even. Roundover bit is nice for body edge, finish doesn't stay long on sharp 90 degree edges, elsewise use binding. Plunge bits for cavities. But Forstner bit on a regular drill is good for hogging out wood, just not as purty.
Clamps, clamps and more clamps. all kinds, types and shapes come in handy. I personally like the "Quick grip" style with the rubber pads on the gripping surfaces. I use yellow carpenter's glue, tacks good, dries ok and doesn't creep too badly. I spilt a whole bottle of that crap on my table which then dripped onto the carpet, thankfully its water soluble.
Sure you can build a guitar with what you got. Sandpaper works faster on a dual action sander tho. But I would definitely get a set of rasps, they are relatively cheap and are really easy to use. Best shaping tool I ever used.