You'll need to move your music from your PC to the Mac.
For your apps:
Open up iTunes and authorize it with your existing Apple ID. You'll find it under 'Store' on the menu bar.
Then head for iTunes Store in the sidebar.
Once there, on the right sidebar in the store, under Quick Links, you'll find an itme called Purchases. Click on that and it will take you to a screen where you'll be able to re-download only selected or all apps that you've ever purchased.
As for your Contacts:
After you connect your iPhone, head for the Info tab - put a check in the Sync Contacts box there. Read over the options provided. The first time you sync, it should ask if you want to replace/merge the contacts from the phone to your Mac.
"Assuming" you haven't gotten rid of your PC yet, I'd sync it there one last time making sure to do a backup - always, just in case.
And if you're getting rid of the PC, make sure to go into iTunes and Deauthorize the iTunes account on it.