My two cents:

Clean with some solution to get off grime/dust if needed.

- Yes. The go-to is something called TSP. You can buy it in powder form and mix it or just buy it in liquid form.

Sand lightly with 120 grit sanding block or orbital sander

- Let dry first. If you have loose or bad paint then knock that off first with a 5in1 tool or putty knife. Then use a finish sander and sanding block to get a light scuff on the surface. Be sure to caulk any seams or gaps. If you have other imperfections you'll need to fill them in with wood filler and sand smooth.

Wipe away sand with moist towel or microfiber cloth

- I'd vacuum it first, then wipe it down. They make tack clothes for the wipe, but they can get pricey if you use a lot of them so I think you're ok with the towel.

Apply primer

- Yes.

Sand with ~200 grit after priming slightly to smooth it out

- Not really necessary if apply your primer well - no drips, etc.

Apply first coat of paint, brush around edges and 4 inch roller (or similar) for larger flat surfaces. Use roller as much as possible. Let dry.

- As others have said, oil has a great finish but can be tough to work with. Latex is easier, but generally not as nice of a finish. But there are now urethane alkyd paints, which give you easy latex cleanup and application with an oil like finish. Almost all the major brands have them. This is what I would use.

Sand lightly again?

- See below.

Apply second coat of paint and let dry

- Get your primer tinted to the color of your paint and a second coat of paint won't be necessary.

Put on some kind of finish/sealer/polyurethane?

- No, don't bother.