I second also not using GoDaddy - if for no other reason than when the parking page they put on the domain is nothing but a big ad for their company. C'mon: I just paid for it the domain, it's mine, I don't want you putting ads on it just because it's free. Ya know?
Whatever you do, DO NOT use Network Solutions to search for a domain and see if it's available. Once you hit 'enter' in the search field, NetSol puts a lock on it for several days where you cannot buy it somewhere else and they own some sort of rights to it. I don't like shady practices like that myself... Use Internic.com to see if a domain is available, then go to preferred registrar to buy it.