I strongly recommend registering your domain name with a different company than you host with. Doing so allows you to change either company without a potential interruption of service.
If you host and register with the same company, and you decide you want to change web hosts, you have to tell the old company fairly early in the process (since you'll want your domain name pointed at your new host) but it might take three days for the transition to complete. During the transition period, the old hosting provider can screw with you...
If you have them separate, the domain registrar won't care (has no profit motive) when you change web hosts, and you don't have to tell the old host you are changing until AFTER the transition is over. With a domain registrar change, you don't have to transition web hosts while also changing names (well worth it in my experience).
Total cost to do it my way? $10-$15 per year. Honestly, not much of a problem for most people.