We have had hardwood in the foyer for 29 years...still looks beautiful.

Do the hardwood and get a large indoor/outdoor rug for a door mat. I live in New England and this works fine for me.

I chose tile for the foyer because I don't like worrying about the snow coming in during the winter. I found in a previous home with hardwood and a rug, guests would often place their snow boots on the wood rather than the rug. I never understood that but, in this house, I solved that problem by choosing the same tile I have in the bathrooms and laundry room for the foyer.

If there isn't a natural break to change the floors I would recommend doing the hardwood straight through.

You can always do ceramic "hardwood". You can achieve the same look as hardwood, but it's of course, tile.

I do not think it matters as everyone puts a rug down. Back in the day we had Fieldstone and it alwyas looked wonderful. Just swept it.