Yes you do need to prime! I’ve worked in a paint store for a few years, & priming is VERY important for good adhesion of the TWO topcoats of paint you’ll put over the primer.
If you’re using a light color, a white primer is fine, but if you’re using a dark color like burgundy, you have to use GRAY primer followed by 3 coats of the red/burgundy.
Fill nailholes first, sand any rough spots when filler is dry, prime, then finally…the topcoats of paint!
Thanks,
Faron