The people I know who have been successful at this (and they REALLY have been successful!) focus mostly on iPhone 4 and 4S repairs, then 3GS repairs, then i5 repairs. Since the iPhone 5 is still less than a year old, many people are covered under Apple Care, so most repairs need to be done on older devices. Screens are BY FAR the most prominent repairs. Most of your clients will have shattered their screens.
If you intend to stick with this business idea for awhile, you really can't go wrong with stocking up on 4S, 4, and 3GS screens (with the most repairs likely coming from the 4S). i5 screens are good to have, but they are more expensive, and as I said earlier, may not pay off as much.
As for other repairs, the most common ones will likely be as follows (in descending order):
iPhone 4/4S Rear Panel
iPhone 4/4S Battery
iPhone 3GS Battery
iPhone 4/4S Home Button
iPhone 4/4S Dock Connector
Ideally, you would have every part in stock, but realistically, stocking up on screens, rear panels, some batteries, and a few home buttons and dock connectors should get you through 95% of your initial customers. As you learn more about the demand, you will quickly be able to adapt and purchase the right parts at the right time.
Best of luck! Happy Fixing!
http://www.ifixit.com/iPhone-Parts/iPhone-4S
