This page groups a few tips concerning Thunderbird.

To share one's profile between a Windows and a Linux machine (actually, whatever OS !), a solution is to put the profile in a shared directory ;-) To do so, launch thunderbird with the profilemanager option

thunderbird -profilemanager

and then, create a new profile & configure its directory.

Gmail settings

pop.gmail.com, SSL always
imap.gmail.com, SSL always, settings for Thunderbird
smtp.gmail.com, TLS always, port 587, with authentication