Wait, Garden Gnome, do we live next door?? Same issues--dogs that come inside to main living area, lots of gravel dust when windows open, or not open; lots of issues with allegens, wanting something that is super durable, easy to clean and looks nice--and doesn't break the bank! We just (last month) replaced the entry tile & library carpet (yuck) with vinyl click together tiles that look like stone, are seamless, waterproof, feel good underneath, and are guaranteed for life in residential settings. LOVE it!
We had replaced the original linoleum (sheet) in the kitchen/eating area and the living room carpet with a wood looking laminate 6yrs ago. Our installer said that laminate holds up better to dog nails and grit. Our only issue with it has been water can damage it so we have to be super careful. We also put it in the bedroom that I use for sewing.
Right now we have installation of a blonde wood looking laminate going into the basement rec room/quilting studio. I can hardly wait (especially since I can't LA until it's done!). Choose the laminate cause it's better about moisture than it was 6 years ago; thicker so will give more warmth when I'm working down there (over the vinyl) and we don't have to worry as much about any dips in the concrete as much as the vinyl.
We do use a roomba and the laminate, vinyl tiles are perfect. We do have carpet in the bedrooms and on the stairwells--I like the carpet to help me keep stable on the stairs (knees replaced).
I do wear shoes (Alegria, new Brands, Finns, Merricks) when I am going to stand (cooking/LA, etc)