I strongly prefer it being managed so I don't really have to worry about server maintenance and such.
I don't host anything too crazy. I'm a web designer and currently have about 15 sites I'm hosting for clients, with a handful of them being WordPress sites, and the rest, simple HTML informational sites.
Generally "managed" means you share the login details to your host with somebody, they apply updates, they help work with you to tune your server, and they let you know of upcoming problems.
Although there are providers who both offer hosts and offer the management you might find a decent compromise is to pay for them separately.
I remotely manage a lot of servers (40-80) in exchange for an ongoing minimal fee, and I'm not alone in that I expect.
I don't host anything too crazy. I'm a web designer and currently have about 15 sites I'm hosting for clients, with a handful of them being WordPress sites, and the rest, simple HTML informational sites.