I host my own stuff on my server here at home. Although I'm thinking it might be time to go with a paid service of some sort soon.
It really depends on what sort of content you're looking to post. If you just want a blog site of some kind, go with one of the popular blog tools like Blogger or LiveJournal. If you want something that you can put a forum up on, you're going to need something that has a database of some kind. Most often MySQL is the offered choice, but some also offer Postgres SQL.
If you're keen on having your own domain there are a couple places that offer deals on hosting + domain too.
I guess the real questions are:
1) what do you plan on doing with the hosting? - blog, WoW guild site, forums, pics/family stuff, etc
2) how much traffic are you expecting to get? - blogs and family stuff tend to be pretty low traffic, things like forums and guild sites can be higher traffic depending on the popularity
3) what are the hosting providers terms of service/fees? - If you're planning on a site that's more uh, shall we say risque, then some hosting providers won't accept your business. Also check out things like costs for bandwidth over charges, etc. some hosts are cheap up front then sneak on a crap tonne of extra charges.
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