Hi Dave, welcome to PCHF!
Here are some tips when choosing a webhost:
1. Never choose a webhost that offers "unlimited" webspace or bandwidth. These probably aren't professional hosting companies. There are a lot of very small hosting companies out there, being run from garages, that just can't provide very good service. These are the companies that have "unlimited" plans, trying to attract customers.
2. Look for a phone number. If there's no phone number to be found, it's not a real comapny.
3. Send them an email, asking some questions like "What is your uptime?", "What kind of servers do you run?". You don't have to know what these questions mean, but they do. If they don't know how to answer those questions, or they answer very slowly, I'd stay away from them.
4. You'll need tech support when you first start out, I know I did. Look for a host that offers a good ammount of webspace and bandwidth, but not at a ridiculously low price. If the price is too low, chances are they won't be able to provide the best tech support.
4. Look for a host that has "cPanel". cPanel is a control panel that will make things much easier for you. I'd never use a host that dosn't have it.
Here are some webhosting companies I've dealt with in the past.
Chronic Hosting - I'd recommend the starter plan for you. Excellent tech support, they have many tech support reps, and the owner even helps you with tech support. I've used them for over a year now.
PolurNET - Very good ammount of space. They also have very good tech support. I've used them for a few months now.
Whatever you choose, make sure to search google for reviews. Another good site to look for reviews is
http://webhostingtalk.com.
Good Luck!