There are literally hundreds of web hosting companies. Some good, some bad, and only a few that are great.
If you are looking for inexpensive, reliable WordPress hosting (or hosting for just about any type of site really), I highly recommend BlueHost.
The uptime and speed of their servers is fantastic, even on their cheapest hosting plan. Perhaps most importantly though, is that their support goes above and beyond to help you with any issues. This may not seem important now, but after having some bad experiences with other hosting companies I can tell you that it is more than frustrating not to have any help with your site!
If you need help getting WordPress installed with BlueHost, I suggest you make your way over to this fantastic how to start a blog tutorial put together by Scott Chow. He walks you step-by-step through the process of setting up a blog, and it’s absolutely free as well.