Industrial grade carpet tiles would be better. When they show signs of wear, which is inevitable, you only need to replace the affected tiles. The other way is to include a contracting colour carpet in the high-wear areas, such as in a semi-circle around doorways. That also allows you to replace a worn area without having to replace the whole carpet.
Again, use industrial grade continuous flooring. It usually contains granite particles, or similar, to provide grip and improve wear. This will be the easiest to keep clean and almost certainly the hardest wearing. I have some in my factories that is 15 years old and it still looks good, while epoxy floor paints, put down at the same time, have had to be replaced.
Noisy and liable to damage, particularly if laid on wood.
For the stairs, you could also consider pre-formed metal or GPR step covers, which incorporate anti-slip coatings or anti-slip strips on the nosings. They can also have an integral high-visibility nosing. If you choose not to have a high-visibility nosing, take care to ensure that the stair lighting is not too flat. It is much safer if the lighting creates a shadow at the back of the step, with the nosing highlighted.
Colin Bignell