I guess I don't understand the question. In your photo the tile looks fine, the grout lines need work. Why not just clean up the grout either seal it or regrout it? There are tons of products sold that reglaze tile (and grout together but they are best put on by professionals because of their toxicity). So long as the area is lightly used it should last for quite a long time. If the area is heavily used most of these will only be good for a year or two. If you don't like the tile itself, there are tons of places that sell beautiful tiles.

I'm going to guess this house was originally built in the 60's (or so)? If so...there is no match. These types of 'flagstone' like floors were common back then. They used broken stone or tile from other jobs to 'create' a custom floor. If you REALLY want to do this, you are welcome to hire a geologist to name the stone and offer up 'locations' where it might be found...and then see if any stone yards in that location would have anything like it lying around. Just for fun, when was the house built?

Love Edgecomb Gray - it is such a versatile color! To answer your questions... 1. I wouldn't wait to do everything at once and would do the entryway tile first. I would pick a simple and versatile tile for the entryway that will go well with any kitchen tile when the time is right to redo that. 2. A beige, white or off white tile would look great in this space. It would pair perfectly with the beige kitchen tile you have now, yet would look great with any other color as well. This will let you make the change you are looking for now without limiting your options when you redo the kitchen in the future. Here are some links for tile inspiration and great options for your entryway! The Zero Design Collection is very, very popular and extremely versatile. Icon Bone White and Matieres De Rex Sable are also amazing options that would look great with both Edgecomb Gray and your beige kitchen tile. Zero Design Search Results White, Inexpensive Tile Search Results Icon Bone White Matieres De Rex Sable

Also paint colors! My daughter would like a very light rose mauve on the walls.