Would definitely pick different colors and different directions. Please post pictures to help you better with selection.

Would go with lighter color in kitchen, maybe chevron patern? What is counter top, backslash colors?

lets see the engineered flooring you have.

if you want gray, maybe just a porcelain tile done in your herringbone? these are porcelain from Lowes, but look like gray slate

these two are from tilebar and have the wood-look.

you could also get some hex tiles, in porcelain or ceramic, and 'blend' them with your existing wood flooring,,,similar to this (this is marble, but you get the idea)

if you click on the 'more info' link and read through the comments, sometimes they list what products were used. I don't know where you got Pic 1, but you can go back and check the comments to see if they list the product.

Pic #2 is porcelain tile, this tile is very similar to a tile made by Julian Tile, ALAR160 Argento 12" x 24" . that's what was listed in the comments.

Real hardwood next to "wood look" tile only makes the faux hardwood look even more fake ( or faux :) ) . Not a good combo.

Agree with K Laurence, we always try to sway our clients away from doing that.

it's a porcelain tile that just looks like a gray tile.

you can also use natural slate tile as well. I've had it in my kitchen for 12 years and really like it. I've sealed it about 5 times over the years. It's easy to clean and slate does not act like ceramic or porcelain when it's cold. It stays at a room temperature all the time.

If you get a gauged slate ( gauged means the tiles are of equal size and evenness) they look nice and are easy to lay.

The colors can range from light grays to deep blacks. An enhancing sealer will deepen the tones if you prefer.

for instance, this is a gauged black slate in a 12x24

Gauged Montauk Black Slate Tile, Sample · More Info

or in this type of layout

(tile comes in 6 sizes. http://www.homedepot.com/p/MS-International-Hampshire-12-in-x-12-in-Gauged-Slate-Floor-and-Wall-Tile-10-sq-ft-case-SHAM1212/202508363)

Slate is also inexpensive. just something to look at while you're deciding.

here is what it looks like next to wood flooring

Michigan is no different than NY or Ohio...... run the hardwood into the kitchen : ) Your home will look twice the size.

its the grit that is the killer. if you can keep grit at the door you'll be ahead of the game. giant mats, changed frequently, and no shoes/boots off the mat.

if you want to match the wood from the rest of the room, just get more of the same. or do you plan on replacing the entire room? solid hardwood can be refinished multiple times. engineered, once or twice. engineered is probably better suited for a kitchen as it's a bit more stable and resists warping from contact w/moisture better than solid.

Does anyone have any advice on flooring for a basement that has hardwood floors leading down into it? I would like to do porcelain wood look tile but am also concerned about it looking odd next to the oak stairs.

not much you can do about that. you could get a porcelain tile that is similar in color, do a diff tile altogether, or carpet the stairs OR, you could even paint the stair treads/risers.

Match an engineered hardwood product to the oak hardwood. Tile just makes a basement colder.