The music on computer 2 won't be erased but the music on the iPod will be erased. If this music was purchased through iTunes and all through the same Apple ID then they can be downloaded onto the computer through the iTunes store. For non-protected music on computer 1 you can just make a back up copy cd then load that cd onto computer 2. For any protected music you would need to make certain it was purchased through the same Apple ID and that computer...

The first sync will ASK you if you wish to merge your iPhone calendars and address book with your Mac's data.
Also, before you actually sync, you can use the "File" --> "Transfer purchases from christine's iPhone" command to transfer all your apps and purchased music into iTunes. You will need to activate the iTunes account on the computer (use the "Store" menu) before you can do so, though.
Besides there...