Hi Joshua,
Thank you for your post.
According to your description, I understand that you subscribed Office 365 Professional and Small Business mainly for Exchange Online and Lync Online services, however, you want to still keep your website with your current hosting provider Godaddy. If there is any misunderstanding, please feel free to post.
To achieve above scenario, we can create an A record that points to the IP address for your website. For more detailed information, please refer to the following links:
Move your email to Office 365 and keep your current public-facing website
http://onlinehelp.microsoft.com/en-us/office365-smallbusinesses/hh335299.aspx
Update DNS records to keep your website with your current hosting provider
http://onlinehelp.microsoft.com/en-us/office365-smallbusinesses/hh335298.aspx
Thanks,
Jolin Qiao