You absolutely don't want grout there for a reason - when the plane shifts and expands, as it will, grout would crack open. That's why you use a colored silicon caulk that matches your grout (all grout companies make it). Don't use grout and cover it with caulk as this defeats the purpose and you'll just have a caulk-coated crack. Hang the bottom row of tile the same distance above the counter as your grout joints, and that joint will just look like another grout line: I'd agree re. the quarter-round trim - I'd fear wood would get wet too often in that area, discolor and ultimately rot away, or else hide wipedown crud underneath it as it loosens over time. :-/

what do you like? The cabinets are going to be the "in for the long haul" element. Dark counters with a little sparkle can look great, or lightish as well....I wouldn't worry about the floor.....mats end up on tile[hardness] and potentially someone would swap the tile for a more resilient product in the future, but be inclined to leave good cabinets...so I'd see what would be appealing with the cabs. What is the style of the cabs?....the stain sounds warm and nice.

Get a sample of your cabinet doors, and then bring it to visit the samples of counters in your favorite show room. Nobody can guess.

Thank you everyone who responded so far. I really appreciate it. I would really appreciate If anyone can also share some good subway tile examples that may go well in my kitchen. Also, I was thinking about getting a single quartz stone just to avoid the too many grout lines (May be white with some brown/grey vein). Do you think it will look good?