Hi there I have an idea of what I want to call my new business but I don't know the best domain site to search for it, there seems to be so many out there.
I would say try with those who are the bigger registrar companies. From cheaper to expensive I would mention: www.name.com www.oneandone.com www.domainsite.com www.dynadot.com www.mydomain.com www.godaddy.com
To search use who.is or domaintools.com They don't log your search and register the domain before you can To register, it's a toss up. 1and1.com is cheap and has private registration, but the support sucks. GoDaddy is what I use.
search it at whoisn.com they don't log searches. If it's only domain names register it with 1and1, they are cheap and whois privacy is free. their supports really sucks but with only domains I don't think you gonna need much support from them. Good Luck,
The whois info given above is right on to research a domain. As fas as purchasing, I only use GoDaddy. Their prices are inexpensive and their customer service is impressive.