Just a little ceramic information to share as a potter. Vitrified simply means the clay has become glass like by being fired to its proper maturing temperature. Usually ceramic tile means it is a lower temperature clay like earthenware or terra cotta. Porcelain is fired to the highest temperature and is more vitrified if you will. This usually means it is less porous to to absorb water and harder. Low fired ceramics with glazes much darker or lighter than the clay body will show chips easier. Rectified has to do with making the edges precise enough to fit smoothly together for less grout lines. So porcelain cost more to produce but it is more sturdy. All clay tiles should be vitrified.

I second patricia, make it all the same flooring. I did the 'wood floor in the walk in closet' while the rest was tile, ended up taking it out and just tiling everything, the threshold was collecting dust and grime and annoying for my laundry cart.

Is the tile for the flooring? I would recommend long rectangular plank tiles, there are many different looks available here is an example of one project we did that gave the client a neutral design option, they are tiles that look like a textured wood.

Hello. As you rightly mentioned, there are lots of varieties of tiles available in the market today, including the wooden pattern ones. These designs are offered by almost all the leading tile companies. Well, the patterns/designs are usually on individual's preference, but a natural teak wood pattern would give a natural look as you requested. More than the designs of the tiles, the points that I would suggest to take care of before choosing a pattern is 1. It should not be too dark as it will make the room look smaller 2. It can have a decent amount of texture finish, but shouldn't be over board as it will be a hindrance to walk freely and also cleaning would be a pain. 3 The thickness of the tile, many good companies be of standard quality 4. Easy availability of the tile, in case you have to replace the broken tiles, they should be easily available. About matching the floor with your walls and ceiling, do not replicate what is on the floor (color/pattern), instead go for something lighter in shades (wallpapers or paints) for walls and for ceiling you can consider the wooden theme PVC panels, which are available in multiple colors.