Having owned and bought lots of early 60's p basses over the years here's my advice. Keep the original pickguard for sure. I probably wouldn't do a sunburst, even from Riggio, as those never look quite right compared to the originals + years of fading. Sunburst is the most common finish out there, since it's stripped you have a chance to do something else. Pick a period correct color from 61. Pick a color that is less popular, making it more unique.
I would NOT do oly white, black (common) or lake placid (blue and red tort yuck.) Probably not CAR either since no green guard and saturated red on red is too much.. red. Probably not fiesta red either, as that is a super popular refin color (although looks great with tort). Also not sonic or daphne blue, again red and blue. Not a fan of seafoam. That narrows down my list to:
Shoreline gold
Tahitian Coral (fiesta alternative)
Surf Green
Inca Silver
Burgundy Mist
Or just leave it as is, that grain is pretty sweet on there and matches the vibe of the frankenstein headstock repair. Stripped natural are super easy to sell because people can refinish to the exact color they want.
If this were "my" bass I'd probably do sherwood, heavy yellowed shoreline, tahitian, or burgundy. But don't do sherwood as I'm having a 1963 refinished in sherwood atm

If you had a green nitrate guard this list would be totally different.