For a paint finish, things haven't changed much over the years. Although a bright finish (varnish,shellac,oil) shows off the wood to advantage, some pieces call for the opaque finish of paint. Especially things made of ordinary lumberyard wood (pine) as opposed to expensive hardwood.
For openers, fill cracks, gaps in joints and finishing nail holes with wood filler. Smooth the wood filler with a putty knife. Give the filler some time to dry and then sand the whole thing. Walmart has Black & Decker 1/4 sheet orbital sanders for $30. The power tool takes a lot of the curse out of sanding. 120 grit paper is about right, coarse enough to cut the wood and fine enough that the scratches won't show thru the first coat.
First coat is thinned down shellac, to act as a sealer. The grain in wood is layers of harder and softer wood. The softwood soaks up more paint than the hardwood and causes the grain to show thru the paint layers. The sealer soaks into the soft and hard wood, and prevents to top color coat from soaking deeply into the wood. You take plain store bought shellac and cut it 50-50 with shellac thinner (denatured alcohol). The thinned shellac will soak deeply into the fresh wood.
Let the shellac dry hard, overnight at least. Although shellac dries tack free in less than an hour, you want to give it plenty of time to get good and hard so it won't clog the sandpaper when you sand it. The dries shellac coat will be rough to the touch. What's happened is tiny wood fibers that were soft and flexible have gotten hard and bristly thru the shellac drying and hardening then. Sand every thing with 220 grit sand paper until it feels glass smooth. If the sandpaper cuts down thru the shellac to the wood it doesn't matter much, the thinned shellac is still in the wood pores.
Wipe down the sanded piece with a rag dampened in mineral spirits to catch all the sanding dust and then put on the first coat of paint. I don't trust water based or latex paint. I look for a gloss oil based paint. Rust Oleum or Larcaloid has worked for me, but any oil based gloss enamel works. Avoid lacquer unless you have a paint sprayer. Lacquer dries so fast that the brushmarks don't have time to level. Lest the paint dry over night.
Sand the first coat of paint with 220 grit. Wipe the dust down with the same rag moistened in mineral spirits. Then apply t he second coat, let dry and you are done, if you want a glossy surface. For a more sophisticated matte finish, you sand the last coat with 220 grit and then give it a coat of paste wax. Butcher's wax is good. Avoid car wax, it contains silicone to which nothing will ever stick, making a recoat in later years peel off.