For base board, I use a LIGHT gauge nail and shoot the fucknout of it.
You can actually cover it up with paint if you go light enough.
If I dont have that option (5/8 board, or a lath and plaster) I'll go with glazing putty.
No.58 or some shit.
Will never shrink and takes the paint well.
But honestly, dap will do it unless you have some pretty decent gaps and holes.
You'll only get noticable shrinkage for large ones
Drydex like
@HIGHRISK mentioned works great.
Just dont go too hard on the sanding, nice light grain sponge or you'll just expose your hole again.