A larger rug will work fine so long as there is no corner of it in front of a doorway, and no edge bleeding into the natural path. People don't have any trouble stepping on and off the sides of a rug while moving through a space, but it throws off the scheme and confuses the walker to have to walk half on and half off the rug, or to choose to shift off the middle of the natural path to walk either on or off it. I'm not a fan of white walls with brown furniture in traditionally scaled rooms. I think it makes enlivening the scheme and balancing the colors much harder, and looks too much like an apartment, unless there is major architectural drama in the space.

A trick I used for brick/tile was overlaying with non sanded tile grout. Then painted it. I didn't want the brick to show at all. Am assuming here that your brick is thin. Even wall board paste would work, sealed and painted. The other is to just remove the brick, a big job, then recover with wall board. I just prefer no brick at all. As for the doors, painting is a huge task. You may want to reface if money/time is there. Or paint the bottom doors only and cut opening in the top ones for glass or another material. You could also insert panels within the trim. One of my favorite kitchens is from the set of Two and a Half Men, they painted the doors two different colors (insert/outside trim). Kitchen doors always take a lot of work, but many here have done some wonderful redos of existing cupboards with instructions on how they did so. I'm not great on colors, they are a personal touch. My kitchen is terracotta, off the grid of most. One of the kitchens here was with black cupboards on the bottom and top ones a contrast. Loved that kitchen.

Seeing as it is now 5 years since you posted, you will probably never see this, but I have just been sitting and staring transfixed at the sparkles in my Alaska White counter top. We just put in track lighting on a 7 ft. 6 in ceiling with 3500K LED flood lights. It is showing the sparkles pretty well. I find 2700K to be dingy looking and anything over the 3500K to be too cool. Getting into the 6500 range, which they often call "daylight" looks absolutely garish to me. Would like to see the effect of halogen on the sparkles, but they use so much electricity! Oh well.

Admittedly not a good photographer, and these may not be great photos of the space, but SHAKER BEIGE walls in day light. I know people say it has a pink/grey to it but I most definitely do NOT see any pink or grey. I do like it a LOT though. Very warm, very easy to live with and I love how it looks with blue.:)