Bandwidth depends on the traffic you get but proxies take a lot of. As for the space, probably less than 5 mb.
Depending on the script that you'll be using and the functionality it supports, you may even need under 5MB to host your website on, although many webhosts offer generous packages at accessible pricing plans. Watch for the bandwidth allowance as it will surely become a key point if and once your website takes off and becomes big. You definitely don't need to worry about anything at the startup. Check only to make sure that the hosting server fully supports the script.
Well it not depend on your space. But the bandwidth is important the higher the better. And other than that,your server must be have at least 8GB ram coz proxy is a high resources script