My midwives suggested that I make up the bed with a set of clean sheets, then put down a shower curtain, then another set of sheets. That way, after baby is born, you can just strip off the dirty top set of sheets, and crawl into a clean bed.
The carpet can be covered with a drop cloth, as others suggested, or I've heard of people using old quilts...?
I also gave birth in the water at home (lovely choice!

) but I used my own bath tub, so that wasn't an issue so much for me.
As far as chills after birth - get someone to put some blankets in the dryer when baby is just about here, both for you and the little one. They feel WONDERFUL!!!
All the best for a great birth!
__________________
Me

DH
And our three little

, ages 5, 3, and 1, and one little bean! Hoping for another