Would this require a rather expensive proxy server to efficiently and quickly service all requests? Or could we pull this off with a server with about a gigabyte of memory? Thanks.
If you're talking about a caching proxy like squid, then it's mostly based on how large of a cache size you want. Check out Last.fm Blog's awesome Squid guide.
Edit: a load-balancer proxy for a site like HAProxy or LVS can handle quite a few more connections, in the tens of thousands of sustained connections per GB of RAM.