When it comes to adult content, and shared hosting, the thing to check for is the LiteSpeed web server. Adult is not allowed on LiteSpeed. So you have to find a web host that doesn't use this, which isn't many of the best hosts. For adult shared hosting, I would suggest
Hostdime.
Now if you want a VPS, it depends on if you want management and what the budget range is (expectations should match budget!). And it also can't run LiteSpeed. We use
EuroVPS and
Liquidweb for the most important sites. And we use Stablehost and
Evolucix for the slave servers. Ninjahawk is used for test systems. Those are all great VPS hosts. But you need to know enough to manage servers, else that won't end well.