Painting over stained shoe molding

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. :)

There needs to be a 1/4" gap next to all walls to allow the flooring room to expand.

This gap should be covered with trim of some sort. The problem with baseboard alone, is that most baseboard is 3/8" thick, leaving only an 1/8" of an inch for the wood to contract without exposing the edge. This also assumes that the flooring is laid with tremendous precision, which it is likely not.

So your options are:

1. Find thicker baseboards. Door and window casing comes in 3/4" thickness and can be used.
2. Use quarter round or shoe molding to thicken the baseboard.
3. Use door stop in the same way you would use shoe molding.
4. Undercut the drywall so the flooring can expand underneath and use regular baseboard (thanks Matthew)

I had the 3rd option done in my basement, and it turned out pretty nicely.

I would also recommend the caulk. It makes everything look nicer.