I'm in the same boat as the OP. I have have transferred all my music and I have even transferred all my apps after "authorizing" the new computer. I did this by just dragging and dropping using migration assistant to get all my apps into my new iTunes.
Now, I have many 3rd party apps on my iPhone that have a lot of important data in them. How can I ensure that these apps+their data will be transferred over to the new iTunes? How do I do this? What I don't want happening are fresh copies of these apps transferred to my iPhone, thus erasing all my data.
If I click on the "Applications" tab while my iPhone is connected, there is a unchecked box that says "Sync Applications". It's greyed-out, but I can see the list off all the applications I own, with the ones on my iPhone currently checked. If I click on this unchecked box, it says "Are you sure you want to syn applications? All existing applications and their data on the iPhone "My Name's iPhone" will be replaced with applications from this iTunes library." I don't think I want to click on that box, do I? Will this "transfer purchases" option fix this? Or am I past that step already (since I have the apps already on iTunes)?