I LOVE the slate appliances, considered doing them myself but no one in my town sold them and DH is an impulse buyer so we bought appliances the first day we went to look.
As far as wood vs. tile - I chose tile because it is more durable and if you have leaks it is much easier to deal with them having the potential of wood warping and needing replaced. You could always consider the tile that looks like wood. There are some really nice ones out there if you just prefer that look.
Saving your cabinets and redoing them could potentially save you lots of $$. If you want to you could consider just replacing the doors for a more updated look. Just for reference, we bought KraftMaid cabinets from Lowe's for our house. The totally cost would have been ~ $8200 or so but because we had so many problems with them (had previously chose Shenandoah and had to replace them 3 times before we got upgraded) we were given the original price of the other brand which was ~$6300.
I would strongly consider keeping the same layout if you want to stay on a tighter budget. It would cost much more to have to move any electrical/gas/plumbing lines to change the layout.
I'm really not sure what to suggest on the layout. If you took out cabinets you would loose a lot of storage. I know what you mean about the table being in front of the window but right away I'm not seeing what would be better... I will think about that.
One quick thought (I may have more later) is that you can look into tile that LOOKS like wood for the kitchen. (They actually make tile that looks like hardwood.) It may not be something you like, but you can check it out at Lowe's and see if it's something you want to do. That may be a good compromise...of course, I don't know how hard it is to match it with real hardwood in the connecting rooms...
Huge kitchen! Nice. There's so much potential there. I have absolutely no experience with renovations and all I know about kitchen design is my pipe-dream Pinterest photos, but I bet you can do a lot with what you have. Even just replacing the linoleum will instantly update the space. I wonder if you could do an island near where the fridge is and move the fridge somewhere else? As for the cabinets, it seems like you have a ton of them. (Caveat: I live in an apartment with a tiny kitchen.) I wonder if you could tear out some of the cabinets that are on the right side of the picture and put an island or breakfast nook there? Do you also have a pantry? Also, I'm talking out of my butt, so I'd definitely post some questions on H&G.
That kitchen has so much storage! I never heard of slate appliances before (I think I'm behind in terms of house renovation...), but those look really nice. It's true that tile will hold up better in case of leaks, but it's very cold underfoot. It's also really hard (obviously lol), which I don't like if I'm going to be standing in the kitchen for long lengths of time. Wood is easier on the feet and back.