I would assume you'll need one with DHCP and NAT which are basic features you would need to try to avoid.
(No DHCP and you probably cannot initally connect to the expander.)
Stabilty and reliablity are your next concerns.
After that NAT and port forwarding configuration come into play.
Then VPN and DMZ.
You don't need gigabit on your router, you are lucky if you have a base10 connection with your ISP.
You might look at some of the cheap routers to be used in structured wiring.
Gigabit switches are cheap, don't worry about what the switch in the router can do. However if you want convience a 4 port switch on the router can be nice.
$40-80 budget for the router, if you have DSL you may have gotten a 2wire modem/router combo. If thats the case all you need is a switch and you are good to go.