It's possible to just copy the contents of the profile folder from one system to the other; Mozilla's Web site has some instructions on how to move profiles for both Firefox and Thunderbird. However, you can also copy things selectively. If you have Firefox bookmarks that you want to transport from Windows to Linux without having to re-create them manually (which can be a chore), you just need to copy the bookmarks.html file to the proper place in Linux.
The same procedure goes for copying over your Firefox settings, which are stored as the file prefs.js in the same directory. Thunderbird's settings are also stored in a prefs.js file in its own profile directory, and the address book is kept there too in a file named abook.mab. (The address book can also be exported and re-imported by Thunderbird as an LDIF-format text file.)
If you'd rather not mess with these files and just automate the process as much as possible, there is a plug-in for Firefox called FEBE, available on all platforms, that can back up and restore extensions, themes, preferences, cookies and, yes, bookmarks.
Migrating e-mail itself from an existing Windows client into Linux can be a bit of a chore, depending on which application you use. If you're using a mail app that exists in Linux already, such as Thunderbird, the process is not that difficult -- it generally involves little more than copying your old Thunderbird mail directory into the new Thunderbird installation's mail directory.
If you're using Microsoft Outlook or Outlook Express, the process is a little more complicated. There is no direct way to simply import an Outlook mail repository, or .PST, into a Linux mail client. Thunderbird doesn't let you do this, and neither do Evolution or Ximian (at least not yet). Most of this is because of two things: Outlook's proprietary mailbox format, and the fact that Outlook has no native way to export e-mail to standard Unix mailbox formats.
There are ways to work around these problems, though. In Thunderbird's case, you can install a copy of Thunderbird on the same Windows system where you have Outlook running, import Outlook's e-mail into Thunderbird, and then copy Thunderbird's mailboxes to your Linux installation.
I've actually done this by using the PortableApps version of Thunderbird on Windows, which can run Thunderbird from a removable drive without actually installing anything on the Windows machine. (Note that other applications with cross-platform editions, such as OpenOffice.org, exist in PortableApps editions as well, so this trick is not limited to Thunderbird -- you just need to know where the application keeps its settings on both platforms.)
A couple of other programs do exist to help migrate users away from Outlook. One is Outport, which exports Outlook data to a variety of generic formats, but it hasn't been updated in quite some time and seems to exist mostly as a curiosity. Another, more recently updated option is readpst, also designed to export Outlook mail into the standard Unix mbox format, which can be used by Linux mail programs like Kmail.
Finally, I should point out that these examples are specific to these programs. Every other Linux program (or Linux program with a matching Windows edition) stores its settings a little differently, so the migration process will be a little different for each app.