If you'll cut on it, butcher block. Or laminate. ;) I occasionally cut a slice of apple or two on my old stuff, but I hated it and wanted to rip it out. Seriously, don't cut on the counters. Keep a large cutting board stationed near where you prep. As Dianalo mentioned, it's bad on your knives. It dulls them, which leads to more cuts on fingers because a dull knife is a dangerous knife. Given your list, I recommend wood. Thought about that at all? Not shiny, usually not modern, can be rustic, casual, cozy, and not speckled. I have a black walnut island top. I LOVE it. I do not cut directly on it.

Miracle 511 sealers were recommended to me both by my tile store and a few threads I've read on GW. I used Miracle 511 Impregnator on my Ostrich Gray Slate in my laundry room, powder room, not-yet-finished pantry, and entry/foyer. Miracle 511 also makes Seal & Enhance if you prefer an enhanced look. (I considered and tested that enhancer but liked the natural look more.) The sealer is very easy to apply and so far I have absolutely no staining. We haven't subjected the floors it to much, but it has experienced mud, probably grease, and certainly laundry products.

What is the floor you have inside? Tile? Don't laugh, I'm in S Fl where we have lots of tile. Wood? Wood-look tile? Something else? I have always thought that it makes a wonderful extension of your current living space by having the same flooring extend from your living area to the covered patio area. Of course, this only works with certain types of material. Something like the concept below where the folding doors (or sliders) hide completely and the floor extends the living area to the outdoors. ETA: If you can't use the same material, either use a totally different material or use something that has the same color so it blends. Without knowing what you have on the floors in your current home it is hard to say. Here is one where a different material was used extensively for their outdoor areas:

I have had stainless. I now have granite composite for my prep sink and porcelain on cast iron for my clean up sink, both of them in white. The stainless itself was fine but with my hard water I was constantly battling water spots, which got old in a hurry. So for me the granite and porcelain are easier to maintain - or at least, if there are water spots they can’t be seen. Either way - stainless or other material - I think your single bowl, undermount choice is definitely the way to go! I don’t think I will ever go back to a top mount (drop in) double bowl sink!