Domain registration and hosting do not need to be purchased through the same company, so you may like to shop around for domain registration, as prices vary. However, our top recommendation for a hosting company — bluehost.com — offer one free domain name registration with each hosting account, and that is a good option (and you only need the basic hosting package).
Our second recommendation for a hosting company is dreamhost.com. They are slightly more expensive than bluehost.com but they also offer more options for super users if you happen to be one.
Both companies are very reliable in terms of server uptime, have easy-to-navigate interfaces, and provide excellent technical support.
Another hosting company that is very good is hostgator.com.