that is yours, and yours alone.
If you are still using the account that was restored from Time Machine, you may have problems.

Once the new account is created and you have logged in, you will be ready to go.

Make sure that your iTunes account has all the tracks in it that are currently on your iPhone. Hopefully you have not been sharing an iTunes Music Store account. (another potential problem)
Now plug in your iPhone.
iTunes will see it as a new phone and treat it accordingly.

Using your own Apple ID, which hopefully you have, you can set up iCal and Contacts to be your very own.