Cycle isn't quite as effective as it says and creates mini-cycles from what i can tell of using it. If you can find Bio Spira, it costs a bit but should immediately cycle your tank - you can even add your fish with it. Kordon makes a product named Zymbac that can also help, but not as quickly as Bio Spira.
I'm pretty sure that you can leave the carbon in.
The water from the gold fish bowl won't help any since the beneficial bacteria collects in filters and gravel.
Our walmart is always out of them, along with most of the other things.. the manager stinks big at keeping any part of the store stocked & it's the most poorly run walmart that I've seen so congrats on a happy purchase.

We'll look forward to your tank pictures.
Have you thought of what fish you want in it?
EDIT: You'll also want the API freshwater master kit, if you haven't already got it. They should be at your LPS/LFS or you can get them at the Dr. Fosters & Smith website, which has great prices & selection:
http://www.drsfostersmith.com/. And a tap water conditioner - Prime is best, then NovAqua+.