The answer to this question, (like most "I want function X" questions for home routers) may be to get a router which supports DD-WRT and configure the firewall in DD-WRT to only allow access to the IP of the site in question + DNS).
To make the site work, you could probably get away with a set of rules which readdresses any traffic on port 80 to the IP of the website you want. (It looks like you can do this using the NAT/QoS tag). [ Also, block anything except port 80 and 53 traffic ]
[ This will be a 99% solution, you were not clear on "how vital" non-abuse is. If its absolutely vital you need to lock down DNS and force answers for everything to the IP address you want. Similarly if there is more then 1 website on the web server and its imperative that only the 1 you want is reachable, you would need to intercept packets with a proxy and rewrite them - which is comparatively difficult ]