Eric and I have been staring at linoleum swatches for days, and it's very hard to visualize an entire floor based on a tiny square, so I put together these mock-ups, based on our favorite swatches. Bear in mind that the counter will be tiled in white with red detail, and the backsplash will come up almost to the height of the window. Also, there will be a counter running along the left-hand wall, so there will be less floor showing than in these pictures.
This is assuming that we can get the linoleum tiles in small enough squares. Here's what it would look like with bigger squares: