D.M.
To download iTunes, just go to http://www.apple.com/itunes/ and download it. No ID required to download the program.
You can find your Apple ID on your Apple device (you mention an iPod) by going into Settings and then to the Store area under Settings. There you'll find your apple ID.
Failing that, check all your email addresses for an email from Apple looking for any purchase receipts, confirmation emails, newsletters, etc. That will give you your Apple ID, since it's an email address. Failing that, there's a recovery tool where you can get your ID and reset your password. Just have to remember the answers to your security questions.
Generally everything you've purchased will be tied to your account, meaning you can download/install apps to another device so long as you've got your ID and password, and it shouldn't mess with your iPod settings, and should use that for backup information.
EDIT - Jo mentions trying various emails until one sticks. Sometimes that's a good idea, if you've only got two or three of them. Apple will lock you out if you fail after five, and then you get to play the wait until the lock out timer ends game, or call in and prove to them that you're you. Same thing with an iPod. Five failed pass code attempts and the device locks for one minute. To many (haven't tested this, but I got up to a five minute lock out after nine failed attempts before finally remembering my security code), and you'll be locked out for upwards of three days.