I’d probably sand up to p400 and then see how smooth it feels to you. The neck will be a lot smoother than the body was to start with, so don’t start with anything too coarse, especially on the fretboard. Concentrate on getting the marker dot areas smooth, sometimes they can stand a bit proud.

The fine sanding will really be on the finish. You’ll mark the frets and get finish on them, so after finally sanding the board surface finish down, you’ll want to tape it off and then fine sand and polish the frets. If you want a glossy board, then you can do the final board and fret polishing together if you want.

Don’t sand between coats unless you’ve got a lot of dust or dirt sticking to a coat. The coats are thin, and it’s easy to sand off two or more layer thicknesses in one go. Any particle removal sanding needs to be as light as possible and with a fine grit, the finest that will do the job. Start really fine and move to the next grit down until you get a result.