I could ask you to reconsider but it's your furniture. You do you.
Virtually any primer that specifies it's good for bare wood will suffice. If you want a really smooth finish, prime the wood with a thinned coat of primer paint, then come back and sand it gently with fine sandpaper, about 220 grit.
The wood will "fuzz up" when the surface fibers are moistened by the paint's carrier, be it water or solvent. Allow the paint to dry and those raised fibers stick in place. Sand them off but not all the primer, and what's left is all firmly fixed in place by the dried primer.
Then you can prime again, lightly sand if you think it needs it, and then apply your color coats.
It may seem like extra work but you can generate, at home with no fancy equipment whatsoever, an almost automotive-level shine with off-the-shelf materials.
Good luck with it.