First of all, there is no "unlimited" hosting. That's just a marketing trick and an illusion to lure you in. Bandwidth costs, so no company provides it for free. In their TOS, they usually have a "fair usage" disclaimer, which states that in case you overload the server or pass your bandwidth limit, they will either upgrade you or shut you down. This is true for all shared hosts that offer unlimited disk space & bandwidth despite what you may read. The limit on this "unlimited" package is usually 100 GB or 1 TB per month, but it varies with the company. So, if your sites get big enough, you will end up paying for the bandwidth sooner or later, it won't be unlimited.
Second, to make sure that any DMCA complaint papers that you get go straight to the toilet, choose an offshore host, which is more expensive than a normal one. Usually this involves paying for servers that are managed in Panama, Russia, etc... Search on the BHW marketplace, Google or Web hosting Talk and you will find plenty of companies.
Regarding adult, it's a gray area. Most hosting companies are fine with it, as long as it's not illegal. Some others don't accept any adult whatsoever, but in most cases, a normal host would do fine, you don't need an offshore host for adult.
