New Computer. Change from POP3 to IMAP

On my current computer, I use eMClient with a POP3 account and a lot of local folders. I’m about to setup a new computer, and would like to move to an IMAP account and then copy my local folders across.
How should I do this and, particularly, what should I do with the emails still in my Inbox?
Also, how about Calendar and Contacts?
I do regular eMClient backups to an external hard drive.