The typical model for multiplayer FPS in AAA titles these days is peer-to-peer multiplayer (where one player is chosen to be the server, and all others are peers relying on that player for synchronized updates).
You can use this model in an XNA game for the XBOX 360.
You can get started at the networking architecture for XBOX XNA samples.
There are numerous examples including this one that demonstrates the type of network architecture used in AAA FPS titles like Halo and Call of Duty (where there is no dedicated server, except for the server(s) that handle the matchmaking).
One thing that you will be missing is the ability to query a dedicated server when matchmaking players. However, if you get to a point where you have so many players that you would benefit significantly from having a dedicated server for a matchmaking lobby, it's not unreasonable to go to microsoft to get a Live Arcade agreement, in which case you will have access to the microsoft storage servers and potentially access to your own server. Until you get that kind of (pretty large) userbase, peer-to-peer matchmaking will suit your purposes just fine.