Before you transfer data to your new Mac you should backup all those visible folders, and the hidden folders I'm about to mention, to disc or an external or network drive. Even if the migration goes well it's worth having another copy to fall back on if disaster strikes in the future. Some files can be easily downloaded again or ripped from disc, but others might be irreplaceable -- such as family photos, iPhone backups and old email archives which are no longer stored on your mail server. Don't wipe anything from your old Mac until you're confident the migration was successful. Even then don't be in a rush to wipe it, in case you later decide there are specific files or application settings you want to retrieve.
To migrate iTunes to your new Mac, you'll want to copy across ~Library/iTunes to bring across your settings. Also copy ~/Library/Application Support/MobileSync to bring across the backups of your iGadgets. If you dig through this folder you can find hidden backups of the photos and video clips on your iGadgets, which could be a lifesaver one day if disaster strikes your phone.
The final step is to dip into ~Library/Preferences and grab all the .plist files with "iTunes"or "iPod" in the name. Once all the files are in place on your new Mac you should be able to launch iTunes and have it look and feel exactly like the old Mac. When you're satisfied all is well, remember to deauthorise your iTunes account on the old Mac and authorise it on the new one (unless you want to play content purchased from iTunes on both). If you use the iOS Remote app to control iTunes or you sync iTunes to an Apple TV, you'll need to set these up again.
When I plugged my iPhone into the new Mac iTunes was happy, except it said "This computer is no longer authorised" for some of apps stored on the phone. That's only because I forgot to authorise iTunes for my US account, which was easily fixed. iTunes resynced the photo galleries to my phone but didn't replace the apps and their settings remained intact. If you've set an application other than iPhoto to automatically open when you plug in an iGadget, you'll need to set this up again.
If iTunes doesn't recognise your iPhone straight away as one it already knows, stop immediately. You might have missed a configuration file. Don't let iTunes remove apps or set your phone up as a new device. If everything does go pear-shaped and your phone is wiped, don't panic. You can restore it using your backup copy of the ~/Library/Application Support/MobileSync from your old Mac which contains the full iTunes's backup of your iPhone.
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