Yep, definitely use Dreamhost. They rock.
Go to:
https://signup.dreamhost.com/
Select pay yearly, for $119.40.
Use coupon code "MDDR" for $97 off.
Pick the domain you want and leave all other options set their defaults.
Hosting means online webspace. Domains are just a name to point to your webspace.
This setup will give you a domain and a full year of hosting for $22.
After the first year your domain will need to be renewed. This will be $10. Hosting (renting the web space) will be $5.95 / month. So, after the first year (which is $22 total because of the coupon code) the cost will be $6.50 / month for your domain and hosting.