I can't speak for Linksys, but my Netgear cable / DSL router at home does NAT and has a simple port-filtering firewall. By default all incoming ports are blocked (not sure if its literally all- or just the first 1024).

If I want to set up a web hosting machine I can configure it to send port 80 traffic to a specific internal IP address. I can also set up one internal IP address as a catch-all "DMZ" machine where it will allow all traffic while blocking it to the rest of the network.

My understanding is that most of these simple routers (Linksys, DLink, Netgear, Siemens) operate about the same. Check your owners manual or the manufacturer's web site for more details.