Hardwood floor care question??

Hardwood floor care question??
I just removed the carpet in my living room and there are beautiful hardwood floors underneath. I did this in my bedroom too, and stripped all the old adhesive with Jasco Adhesive Remover and put polyurethane back on the floor to protect it.
But that was such a huge undertaking and I'm just not wanting to spend that much time on this one, I have already bought a large area rug which will leave about 1 ft to 2 ft around the edge showing.
My question is this, what is the best soap/cleaner to use to get the leftover residue off the floor and what type of scrubbing device should I use to do it.
Thanks!