Proxy Sites are unique by its own way. Every one of them has more or less the same requirements when it comes to hosting. Quality of the services comes first here. That's because the end users tend to use only reliable proxy sites and what's make a proxy reliable compare to others is the uptime of the service.
What makes a proxy hosting to stand up from the rest apart from the uptime is the proxy hosting packages that it offers. Important thing for a proxy website is the bandwidth. You will not believe your eyes how "easy" it can be to run out of bandwidth if you don't previously set up some standards for your visitors. A couple of proxy hosting providers include GeoIP mod in order to filter traffic from countries with low ad click values and low conversions.