I've been running my own websites since 1996 and have used all sorts of hosting companies over the years. I've been with Dreamhost since 2007, and for a shared hosting company (where you're on a server with a bunch of other domains) they're pretty good. Unlike so many of the hosting companies I've used, these guys know what they're doing, have great support staff, and while neither I (nor they) can promise 100% uptime - they offer UNLIMITED disk space and bandwidth, a fantastic custom written control panel (which kicks cPanels butt), a ton of tools and databases, quick response on problem tickets, one click installs of Wordpress and much more. Here's a list of what you'll get.
I created the following promo code: 75DH2YRL1 which will give you $75 off when you sign up for a 2 year hosting contract (which brings the bill for your first couple years down into the realm of those el-cheapo hosting companies). This is exactly how I got started using them, so I'm happy to offer the savings to others. Disclaimer: I get a little something for my trouble here, but giving you so much means I get less.
note: if you're planning a site for a non-profit, Dreamhost offers FREE hosting for non-profits!