New to web hosting, what hosting services can I use?

Bluehost. Cheap. Excellent wordpress intergration and their customer service has been outstanding.

I am very happy with fatcow. For a cheap service ($3.95/m I believe), their customer service has been superlative. Domain names with them are a bit more expensive ($14.99 instead of $9.99) but I'm actually finding the simplicity of having everything together, with great help by phone or live chat, worth it.

Another happy Nearly Free Speech customer here. I like how cheap it is, the pay-as-you-go nature of the thing, and have learned a lot in getting the Wordpress site up and running. I've since branched out and setup a Twitter archive (a second mySQL instance) and a URL-shortening service (a third mySQL instance) with minimal fuss. I didn't think I'd get that deep into other uses for webhosts, but there you go. Agree with others that it is a bit more work to get things setup (no 'one-click installs'), but it is pennies per day for a low-traffic site.

My advice: Separate your DNS registrar and host from your webhost. This makes it easier to move thing if you get into a dispute with your webhost, or they suddenly go off line or out of business. Continue using Wordpress. no porting necessary, and wordpress provides tools for exporting your content from wordpress.com and importing it into self- or third-party hosted Wordpress.

I'll second Caconym's comments on Nearly Free Speech. I'm playing around with some Wordpress sites hosted there right now. They are dirt cheap for low-traffic sites, but you have to be willing to fart around and read the FAQ a lot to do things that one-click on other hosts. You'll have to get under the hood when you're doing an update or other maintenance. They would certainly be the cheapest option, though, so if you wanted your site to make some extra money as opposed to just covering hosting costs, they might have an advantage.

2nding Bluehost. I've had no problems with them and have used them for multiple sites over the last six years.

Put me down as another generally satisfied Dreamhost customer. I run a very very casual sort of personal site, so the occasional meltdown, as kirkaracha mentions, hasn't really affected me at all. YMMV. They have a one-click install for Wordpress that makes the already simple Wordpress install even easier, and it will automatically update it for you. I've always had great support experiences too, on the rare occasions when I've needed to contact them.

If you just want to run this one WordPress site, a company like Laughing Squid that specializes in WordPress hosting would probably be simplest. I've used DreamHost for over 10 years and generally been happy, but about once a year for the last couple of years or so they've have a complete meltdown and did a very poor job communicating to their customers about it, so I started switching to WebFaction. I've used Dotster and DreamHost for domain names in the past. DreamHost is convenient if you're hosted there because it's one-stop shopping. Lately I've been using Namecheap and I'm happy with them.

I use HostGator for hosting & Namecheap for domain registration and have been very happy with both.