That's going to be a lot of work if you haven't got the experience with linux already. Start studying and playing with linux to learn. If you can, plan a transition where you will have both sets of servers up.
Are your Windows systems XP or Vista or what? And your Windows servers? Roaming profiles or anything that has to be accounted for like that?
You will want a Samba configuration that works as a domain controller. One possibility would be to set up a backup domain controller and then promote it.
You can find howto's and guides through google or use these:
Backup server is another issue. What do you need there? Are you talking about backing up all the Windows machines? Or do they store things on the server and then the server gets backed up? Is it going to tape? Or are you just looking for some way of backing up the directories where people store things? Or backing up the server itself so that it can be recovered?
Mail server starts getting more complicated yet. There are a lot of security issues there. Are you meaning to have a company mail server that all the Windows people use to send and receive both inside and outside mail?