Time Machine is the simplest way to go, otherwise...
a. IMAP/Exchange mailserver: your files stay on the server, changes from the client are made on the server. Your MBP would get all the messages off the server as they were on your other machine. Gmail offers free IMAP.
b. POP mailserver: normally the default is to download the messages (remove from server as downloaded).
c. there must be lots of other ways, like copying over the local mail files, but my laziness prevents me from understanding its ins and outs.
In case of b., with OS X Mail drag mail from POP accounts over to an IMAP account (solution a). But if you can't deal with that, go for door c.