I think this gray faux wood tile will look very nice with brown carpet. It also will look wonderful in an all white kitchen!

If you are seeking a truly open feel to the floor plan you have shared, then using one material in the mail living area is the best approach to making this space feel truly open. Using a variety of materials on flooring chops up the space and decreases the visual footprint. I would suggest using wood, tile, or if you are on a tight budget laminated flooring for the living/dining/kitchen. Then use carpet in the more intimate spaces; bedrooms and possibly hallway. Save the tile for the bathrooms.

Paint your house and ceiling first. You are probably asking for trouble if you put the floors down only to paint over the top of them. If you can, remove the tiles in the kitchen and paint just behind the line of the splashback too. Once painting is done replace kitchen benchtop then splashback. I would call the bathroom its own job and do it individually, unless you only need to paint the ceiling and if a tiler doesn't need to be brought in for anything else in the house? A lot of bathrooms now are getting tiled from floor to the ceiling if this is the case, paint the ceiling first, then tile. If walls need to be painted, it wouldn't really matter if you did them first or last, though if you did it first expect to do some touch-ups. I guess if you really wanted, you could do the first coat before tiles then second after... I don't exactly like stopping and starting painting, so I would do the walls (if they needed to be done) in one hit, after its been tiled. Well that's the order in which I would do everything... Really, for what you're asking, the painting could be done at anytime, but to make life easy on yourself, I would definitely recommend doing it before the floor.

Hope post shows, got some weird error message