Don't be stupid, you don't need a dedicated straight off. Proxies don't go from zero visitors to thousands a day within a few hours of uploading it. I've got a reseller and run two proxies and numerous other sites and it's more than enough. Just make sure your host allows proxies before you go ahead with them.
If you're serious about them, and know how to blow them up big then you don't mess around with shared or VPS for proxy sites.
Proxies get blocked by web filters at schools and work, therefore proxies need to be replaced after some time. Do proxies tend to stay profitable? I think it depends how quickly they get blocked schools and work.
If you can rank good, you can stay very profitable even after being blocked by the common school filters (websense, etc.). ocrig.com is #1 for "myspace proxy" in Google, is obviously blocked by the big filters, but definitely gets better traffic than those that aren't blocked.
The Web proxy business is volatile through many facets: 1. Volatility of accessibility: as the demand gets higher for your proxy (assuming solid, continuous service), it reaches a certain crescendo as countries/schools start to ban your Website and the demand levels off. 2. Volatility of revenue: you can never rely on any ad serving network; they either screw you or you screw them. Something just has to happen. 3. Volatility of technology: as technology improves there might be a point in time where Web proxies are no longer efficacious. Alternatives might also surface. Technology that battles Web proxies might also improve. 4. Volatility of demand: people tend to move to the newer, faster and better. If you don't keep up with the pace of increasing demand and a constant level of service, demand might whither. 5. Volatility of cost: higher demand -> higher bandwidth -> less earnings.
Yeah, I actually been seeing a lot of Web Proxy sites being sold in the For Sale section. Judging by the responses, it seems more like supply outweights demand.