What wallet should I use to collect the mining payout from multiple machines? I am trying to set up my Debian Server so that I can join a mining pool.

I already know that I am going to use cgminer for the mining software because it will work with the server format (command line).

What I am not sure about is what type of wallet I should use and how I would link multiple machines to one wallet (I want to use my home computer as well).
Regardless of what wallet you use, it's entirely unrelated to your mining except as a payout. The address you withdraw to can be in a wallet anywhere (even offline).

P.S. You should really consider upgrading to BFGMiner instead.