I painted all my bedroom trim, baseboard, and crown before install. To me, since the ceilings were so high, it was MUCH easier. One thing to check. Does your wood have knot holes? Despite my urging, my GC brought pine that had knot holes, the best for the price I could afford, and I primed with ordinary primer then painted with an off white satin finish. Well, it didn't take long before those knot holes bled through. Make sure you use a primer especially made to cover knot holes (can't think of the name right now). I had to go back and touch up the trim and baseboard knot holes with the special primer and repaint with another finish coat. That was three years ago and yellow spots are still appearing. :(

You are welcome to put the vinyl over top the marble. Be aware that you will NOT be able to do the preparation needed for the vinyl to be properly installed. The preparation means you have to a SMOOTH and FLAT subfloor (grout lines would, ideally, be level with the tile) and any humps/bumps ground down/flattened and any hollows filled with concrete. Ahhhhhhh. Now you see where this is getting tricky. To "cover" the marble (to "save it") you may have to destroy it to make the vinyl install "proper". If you do NOT do the proper preparation, you will get a vinyl floor that will telegraph ALL THE GROUT LINES through to the surface. You will end up with a "checker board" pattern of grout lines showing through the surface of your newly laid vinyl. Here is my suggestion: Water-Proof LAMINATE! Yep. Something like Aquagard (at several dollars more per square foot) will do it. Why? Aquaguard is RIGID. And it allows UNDERLAYMENT which can help with any minor imperfections. Yes...technically laminate wants a properly prepared subfloor - but it is more forgiving visually. You might get a snick of movement over hollows but I would take a tiny bit of movement over a grid pattern etched into vinyl any day. As for the baseboards....remove them and install something that fits your aesthetics. The one's visible are nothing special. Some of them don't even match the tile they are attached to. Not worth saving in my opinion. Have a look at water proof laminate. It offers the same wearability without the issues with excess heat/direct sunlight and without the issues of a super flat subfloor.

I like the way this house is finished with simple cove crown molding. I like that the molding is white, but the door is stained wood. Where the ceiling is slanted they omitted the crown molding; much cleaner look for that area. The base molding is quite generous.

I also hate the ledge on baseboards. It just catches dirt and I agree it looks tacky in some homes. In a traditional home it looks fine, but then the cleaning is a PITA. There are two options for you: Trimless, and Flush trim. Trimless: In traditional homes trimless is usually only done on outside and inside wall corners, or sometimes around windows with thick walls. This is because of wear and tear. Your robot vacuum will destroy your walls if you drywall all the way to the floor. You will bump the walls in doorways and they will look beat up in the not good way. This brings you to the second option: Flush trim. Look into the "flush to the wall baseboard". It's a high-end look. You can also do this flush trim around windows, doors, closets... You have to buy a little product to make a clean edge transition from the baseboard to your trim, so it costs a little more. Normally your drywall guy can be really sloppy with the bottom edge of the wall, and the finish carpenter covers all the sins with a board afterward. Flush trim baseboard