Re-priming over sanded primer

When you say you can see the brush marks, do you mean that they're actually irregularly surfaced? I mean - are we talking just a visual effect or an actual difference in the depth of the paint?

If the latter, do a skim coat with lightweight joint compound and when it dries, either lightly sand OR smooth with a large, slightly damp sponge, then apply primer.

As for your own brush strokes - orient the roller so the roller bar leads your motion. If you're moving right, put the bar on the right. If you're moving left, put the bar on the left. The most pressure will be on the roller bar side, so keeping that side on the "front" of your motion will mean the lighter touch side (the back) will smooth out the uneven strokes as you pass over it again.

Now if its not a real issue with texture, just that your seams are obvious - then just prime it again with a good HEAVY primer, using the proper brush techniques, and you'll be fine. :)

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.