Look at a low nap carpet like a berber, or something suited to a commercial area like you'd see in a bank or in the hallway at an office or condo building. Wood won't have this issue.

I would recommend the Karastan Metropolitan Collection as a carpet choice. Commercial build with a progressive/contemporary pattern and color palette. All carpets will show wear and get matted down if they are heavily soiled.

Agree with jfcwood. A Berber would work or hardwood.

Make sure you got a quality pad under it . A high quality pad really goes long way to extend carpet's life