Please note that my hosting recommendations are for sites that get less than 500,000 pageviews a month. If you get more traffic than that, contact me for recommendations for more robust plans.
Bluehost is a reliable host with an easy-to-use control panel. They offer only one plan that costs $6.95 $4.95 a month* but you have to pay for a year at a time ($59.40).
If you sign up for Bluehost you don’t need to purchase any of the add-ons they try to get you to buy. Just the hosting account will do fine. You can usually find a coupon for them here.
(Note: This is an affiliate links, so I make a small commission if you order through them. However, I only recommend hosts I’ve had good experiences with.)
You can search http://www.findmyhosting.com/ to research hosting plans. This site includes user reviews and data on the host’s uptime. Uptime is the amount of time the server is up and running during the month. Their guide to Budget Hosting is also helpful: http://www.findmyhosting.com/cheap-web-hosting.htm
I believe both of the hosts listed above give you a free domain. If you want to register the domain elsewhere, I usually use Name Cheap* which charges about $10/year. You can usually knock that down a dollar or two with a RetailMeNot coupon here.
You can either order a plan directly or contact me and I can tell you how to securely give me your credit card information so I can set up the plan for you.