No way are you going to get that anywhere close to your budget.
You are asking for literally 1/2 a server's worth of hard drive space, and more or less an entire dedicated server's worth of bandwidth. The servers I normally provision for shared/reseller hosting have anywhere from 5-10TB of bandwidth, and around 1TB of RAID10 drive space. Most providers I've talked to are pretty close to that.
If you truly want those kinds of specs, not oversold, and not some ridiculous "unlimited" offer, that's going to cost you at least $100/mo. if not more.
I would recommend a cheap Atom server, or some other cheap dedicated server, if you want those specs. Still going to cost you considerably, though.