I would love some opinions on these transition areas in my remodel.

Mudroom - I am thinking tile for water resistance. My question is that the stairs to the basement start in the mudroom. If the basement will be carpet, what should those stairs be?

Basement - I assumed it would be carpet. Will be a kids playroom and there is a guest room also.

2nd floor laundry room - Tile? The hallways will be hardwood

3rd floor workout room - Carpet? Cork? And what should the stairs be? Again, the hallways on the 2nd floor will be hardwood.

Thanks in advance!