It all depends on when you want to use your new server. If you have
MX 20 servername.ispdomain.com
MX 10 newservername.mydomain.com
.. then all mail will go to your new server. If you have
MX 20 servername.ispdomain.com
MX 15 newservername.mydomain.com
MX 10 oldservername.mydomain.com
.. then all mail will go to the old server until that MX record is removed and the new one has the highest priority.
Basically, a few days before you want to change to your new server have the TTL on the zone reduced to say 600 (10 minutes) so that when you change the MX record the changes will propagate within 10 minutes. Once changed over then the TTL can be reverted back to the old value. Changes 'can' take a long time to propagate but if planned correctly there is no need for this.
Chris.
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Chris A.C, CCNA, CCSA
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