You do know that after you have authorized the the phone on the iMac, that you can right click on the phones name in Itunes and select to transfer your purchases to the new computer right?
I was wondering why no one had told the OP this. It's that easy.
OP, what you should also do is backup your iPhone in iTunes to the Mac. That'll bring over the App settings, among other things. Then sync contacts, notes, etc. (you won't be able to get pics, video, and music w/o copying them from the computer to the Mac....make sure to consolidate the library before copying) and you'll be all set. Oh, BTW, if it asks to merge, pick merge.