I would look for a vps of some sorts, I've seen em as low as $20 a month, having a vps is a surefire way of not getting kicked off because of the server load your causing.
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That's just hilarious! Spend some time reading the rules!
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The best thing you can do is get your own VPS and then once you are getting enough traffic move your site to a dedicated server. But if you can't afford the higher prices of VPS or dedicated servers check out hostgator and dreamhost, they arer two reputable hosts that allow you to have a proxy site.