Hello,
Thank you for your question about DNS for transfers. You will want to set up the DNS on the new server to be like the current one. All files and DNS records on the new server will not be in use until you point to that server. This can be done by pointing to our name servers. If you are using a third party DNS, then that will still be the DNS authority and you will simply need to point your individual records to our servers from there.
Kindest Regards,
Scott M