Tile is still the best thing for a walk-in shower to be waterproof. Neither the cork or hardwood will be. Think about installing a radiant floor under the tile like Sharon recommended. I like the NuHeat Radiant floor system the best.

I would suggest you take out the cabinet that is to the right of the stove and use it elsewhere in the house -- perhaps in the bathroom or dining room with a hutch above it. Then, I would suggest you have someone install a lazy susan cabinet in the corner between the sink counter and the stove, meaning you would move the stove down a bit and have a small cabinet/counter top to the right of the stove. I would suggest you have the cabinets refinished in white and then paint the walls a pastel you like. If you would prefer white walls, then add white-painted crown molding and paint the ceiling a light neutral blue, such as Sherwin Williams Niagara Falls Blue. Then, I would suggest you choose a favorite accent color and use this sparingly in accessories like towels, pot holders, small vases or floral arrangements, and a valence above the triple windows. For a genuine 1940s look, you might have white ceramic square tiles with a rectangular red border installed as a back splash behind and above the stove. If you are replacing counter tops, I would suggest a light color such as white with a beige or light grey vein or striation for some sort of pattern. You might be able to find the same color and design in floor tile OR opt for a wood floor as another poster suggested.

If you are looking to keep the "period" look, then I say no. My place is from 1916 & had a gross 1980's reno. I ripped out all the ugly vinyl floor & cheap Sears sink & went with a black hex floor, white subway, dark grey grout on both. Toilet & tub were original, but I got an old "Standard" wall mount sink with chrome legs & towel bars & an antique medicine chest, light fixtures & glass shelving & towel bar off Ebay. My total job...about $5k. Help my tile guy is my neighbor, but those 10, 15, 20k bathrooms were out of the question.

Heating sources here in New Zealand are typically Heat Pump or woodburner. I see a heat pump merely blowing dirt and dust/hair everywhere... keeping it in the air... and distributing it all over. I've run across this: www.thermaskirt.com which is very interesting. It's like a radiator, using hot water to heat, but on each of the walls, at floor (skirting) level. Since we have 3.3m (11ft) ceilings in this addition, it might be the most effective at providing heat where we need it without blowing dirt/dust around.