Just Host meets all of your requirements. Everything is unlimited. They do allow adult websites, as long as they're legal and no copyright issues.
Their support is very nice aswell.
Both Virtual as Dedicated hosting.
Virtual starting at $3,95 - Dedicated at $140
Special Promo: if you scroll down to their footer you'll see a link there "Secret Link", follow it and you'll get another 20% discount ontop of the standard 20% discount. That's right, 40% discount total.