Paint or build first?

[McCreed]

The bridge is my main concern.
I think I'll fit that first, align the neck etc... then disassemble and paint.

This has been my preferred method. I have drilled the pickguard holes both before and after depending on the project, but definitely before for hardware like a bridge.
However one thing I'll add is I do a small countersink to the holes before the finish goes on. Especially if I'm spraying paint.
The countersink removes the square edge at the top of the hole so the paint doesn't collect on the lip.

I use bee's wax to plug the holes when I'm ready to wet sand (have used surfboard wax also). After the wet sanding and polishing is done, and before I start mounting hardware, I will clean up the countersunk holes with an appropriately sized drill bit*, just twisted with my thumb and index finger (no power drill). This will prevent (or at least help prevent) the finish lifting when a screw is turned in.

*I actually use a conical shaped dremel bit for doing this now.