The proper way to move mail in from an email account with over 100,000 messages

[jvc111]

I have 2 different domains, one with Godaddy which hosts our business website and another with Pobox which holds our personal website.  They are both IMAP accounts and when I linked them one of them downloaded 24400 of 50,000 of the oldest emails.  The other 10 of >100,000 emails.  I would have liked to gotten only the most recent 1,000 of each and not be concerned that there is the possibility of losing the ones on the server as we often go back several years in emails for business purposes.  What is the best thing to do to solve this problem?   I searched the forum and found nothing similar.

[jvc111]

So do I need to close the accounts and re-open them after setting up these parameters as what I have now are the oldest messages from both accounts with nothing other than the most recent emails coming in, but I am unable to see emails from last week and beyond.  Do I need to archive most of my emails on the server in order to avoid this problem?