Just Host got it all. Also, it's one of the cheapest and best hosts around. Their awards are real, they have valid sources for them. They also come with an "anytime money back guarantee". Don't like it? Leave them, and you'll get a full refund for the remaining time you paid for, 24/7. You also get a free domain name, which you get to keep if you wish to leave the host at some point. Although I don't think you'll leave it. They earned my trust, their support is extremely fast and i've never experienced any technical issues. Try them, you've got nothing to lose with their anytime money back guarantee, it's no joke ;)
It's not an adult specific host, but they do allow adult content. Shared Hosting going from as low as $3.45 a month and dedicated from $149 a month. Goodluck.