Some things to note about quickplay:
Quickplay starts sending players to your server after 6 players are in your server.
Your server gains ranks in the quickplay system based on player time spent on the server after they are sent there, among other things.
Why if NFO the best for it?
The InterNAP network. After 6 players, a large factor in quickplay deciding to send players to your server is player ping. Our first week up we NEVER emptied out for the weekend(20+ for 3 days straight), I talked to a few players, some half-way across the country with pings of 25. This impressed me very much, and made me happy that I spent the money on our dedicated server with NFO.
These are my findings, nothing here is meant to be taken as fact. Players staying on your server will be the result of good settings, and friendly players.
Order a TF2 server with NFO and get started!
(Note: use 24 player servers for the best matchmaking results, above that and you get a matchmaking penalty)