I am building a webcam w/ HTTP server that will be running from a low-bandwith connection. The content on the site will be changing every 5 to 10 minutes.

Instead of serving files directly from this connection, are there hosting companies that can act as a reverse proxy for my site? Therefore, if nobody is using the site, the local internet connection remains idle. And if I receive 1000 hits all at the same time, only one HTTP GET is required, and the hosting company (on a fat pipe) continues serving the other 999 requests?

This doesn't sound like a very common usage model, but I feel like this would be the optimal solution to my situation.