You get what you pay for in web hosting. Most providers that offer lots of storage and bandwidth for a very small price suspend accounts that actually use the resources they are paying for.
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You'd better go for a VPS package if you plan to host a usually resource-intensive proxy site.
Hosts aren't really willing to host proxy sites on the shared plans as your neighbours may suffer, that being said, look into cheap VPS options, either in the offer section of the forum or from the recommendations of other members, I know that there are discount deals from HostV.com ans Asmallorange.com.
There are separate kind of web hosting called proxy web hosting, so you will be able to find this kind of web hosting easely.
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santrex.net seems to be web hosting that do not afraid to provide such things like proxy and shells and even IRC. I think that they must be ofshore web hosting company. And that fact can be not interested for most web masters
Are you going to offer proxy services to others? If so dedicated server is a must, there are deals within $30-100 range.
You can get a dedicated solution from hqhost.net within this price range. They also offer proxy hosting accounts on their shared plans.