your case might require special attention cos of their nasty DRM
Personally, when I've transferred iTunes data between two computers, I have had no issues with DRM. All you need to do is login to the iTunes store the first time you open a DRM track on the new machine and hey-presto, all your tracks are unlocked again, no "nasty DRM".
Can't speak for the iPhone as I don't store music on mine, but as Ancient Observer says, the Apple support pages / forums are generally worth a quick search. Or if you're near-enough an Apple store, a trip to a "Genius Bar" (appointment recommended to save you waiting !).