Will it matter if one of the computers is a PC and the other is an Apple?
Let me help you understand as the poster'S above did...
EVERYTHING...iPhone, Touch, iPods, iTunes are ALL related to your iTunes ACCOUNT....Not the computer, not a Mac or PC or any other item or program.
ANY item that you purchased, downloaded or installed freely from iTunes to a computer or iPhone or iTouch or iPod using your CURRENT iTunes ACCOUNT can be transferred to any additional computer regardless of make or model up to 5 AUTHORIZED computers that you authorized using the SAME iTunes account.
If you change accounts, make another or use someone else's, then you can't transfer or use their downloads.
Music and videos can be transferred to those AUTHORIZED computers using a thumb drive, external drive or what ever transfer method you use.
Apps can be clicked on in the iTunes store and downloaded for FREE to any of your AUTHORIZED computers that are logged on to that original account. It will ask if you want to purchase it but after you click on the purchase it will say you already own it...do you want to download again.
There is no other way to explain this to you. If you need more assistance then you really need to go
here and read it for yourself instead of repeating your questions. We are willing to assist and answer questions but not reworded questions of answers already provided.
Good Luck and do what we told you and you will be fine.