After staining give a coat of clear finish, sanding it with a fine sandpaper (400G) to remove any raised grain or any dust that may have settled onto the drying finish. This will give you a good base to add your paint and the sanded surface will give it good adhesion. Steel wool has its purpose, but I would not use it here. That's only my opinion. My experience is the steel wool sheds metal bits everywhere, and may be a deal to clean up completely.
After the recommended dry time for the paint is over, give it your final clear coat.
I know this did not answer your question about how long to wait before the top coat, but depending on what brand of paint you use, makes a difference. Each paint container always list how long it needs to dry before the next coat. Many usually only need 8 hours.
If you do not have that, the safe rule of thumb is, 24 hours if oil over oil, 2 days if water over oil. I don't know what to recommend if oil over water.
Yes, you can and should sand latex if you are painting over it. You cannot expect the next coat of paint to grip if it doesn't have a roughed surface to grip to. Painting a glossy or glazed surface is like painting glass - it has no adhesion and will lift right up.
Fresh latex is hard to sand because it hasn't cured yet. You have to wait it out. If it won't sand, it's definitely too soon to overcoat it with anything but itself. (and on that, check the cans for recoat rules). You really need to leave decent curing time between dissimilar products - especially oil over latex.
There is no such thing as paint-primer. Paint companies tell you that to take your money. Their marketing claim is based on painting surfaces which are close to ideal - that is to say, well prepared and primed, with no material variations.
By "material variations" I mean material, color, porosity, chemical differences, anything which might "print through" because the topcoat reacts differently to it. I'm not referring to physical roughness like brush stipple or high spots. The purpose of primer is to bind to the underlying surfaces no matter what they are, seal them, and make them "equal" to the topcoat, so the topcoat applies uniformly and reflects exactly the physical terrain, without visible glitches for any other reason.
Done right, you will not see where wood meets marble, an area was previously painted, or where a cat peed on bare drywall.
You also need to remove surface contaminants which would foul the primer (oil, acids) or prevent adhesion (wax, silicones, linseed oil). In machinery paint, that's the classic 2-cloth wipedown with solvent. Water is a solvent, but too many contaminants are immune to it, so you need to use a chemical solvent or strong soaps, e.g. the classic TSP. You need to get the soap residue off.
Invariably when paint fails, somebody skipped one of these steps.
Why are the oil brush strokes still visible? Is this contamination like acid which is fouling each layer? (remove it). Or is it physical irregularity/bumps (sand it down). A build primer is specifically meant to be sanded. It will leave brush stipple marks far more than a topcoat will, but it's easy to sand.
Best Answer
Painting over a glossy oil paint is indeed different than painting over an oil primer. I just came from a customers's home where the seller did the former - you can literally pull sheets of the paint off the trim. Maybe there are better latex paints that tend to adhere more strongly and you can get away with putting them over oil, but I'd never do it.
Don't take the chance. Either stick with oil-based paint on trim that already has it, or sand and prime first before switching to latex.