Managing Typepad is extremely easy. I've used them extensively in the past for our corporate blog, and been fairly happy with their service. The only complaint I've had is that they're somewhat barebones, feature-wise, in exchange for very high uptime and a very simple user interface.
As far as I know, Typepad doesn't even offer a host-it-yourself service; that's part of their value: they host it for you. The advantage over a service that does do self-hosting (such as Blogger) is that you don't need to worry about maintaining your own server, handling bandwidth, and so on. The downside, obviously, is that you'll pay Typepad rates for hosting media, which are probably a bit higher than what you'd pay for using a shared host.