It looks dirty and the grout is, but those brown specks on tile will not come off

The brown door, beige floor, and gray closet doors don't work at all. Somebody has to go.

The beige floor looks much more interesting in the close-up. But if it cannot be cleaned (have you had a cleaning pro look at it, or just an amateur?), then that would be what needs to go. Since it is the entryway, slapping a rug over it will just scream "I'm a cheap flip. As you go through the rest of the house, look for the rest of the cheap work that has been done."

In today's market, it might not matter.

In today's market, you will find a buyer with the brown door, beige floor, and gray closet doors. And the new owner will eventually decide who needs to go.

I said i was painting walls and trim i will paint doors as well

So what do you want to do with the floor?