I prefer LiveJournal, and I've used Xanga, Blogger, DeadJournal, LiveJournal, EFx2Blog (I believe it is...), and many others.
As for clients for LiveJournal, if you're using FireFox (and/or Mozilla), you can download an extension (Deep Sender) and it makes updating the easiest I believe it can be (which is pretty easy).
For running a blog on your own server, it's a good and bad thing.
Good: You control everything, you can set it exactly the way you like it, no T.O.S.'s (basically)
Bad: Depending on what you do (program your own or use an existing one) you may not get friendly tech support (then again, you may not get that anyways...heh), you have to do all the maintaining instead of someone else, no one to blame for those slow hours (
)
** Some (or all) of these points may not be correct or something...but that's the way I see the pro's and con's of running your own **
Personally, I'd say go with LiveJournal (which is highly customizable...even with the free package), see if you like it. Then, if you want later on, set up your own (there's still some free servers that allow scripts [like lycos.co.uk (PHP4/5)]).
LJ is also a good choice because of the community setup they have. I don't belong to any (yet), but there's really a community for everything.