Yes, do the address change with the USPS online. However, also call and change your address with your credit cards, car loan, insurance, magazines, or anyone else who regularly sends you mail. The mail forwarding is not very good. You should only depend on it to catch mail that falls through the cracks.
I have been getting my ex-husband's mail forwarded to me NOT BY MY CHOICE because they are too dumb to read the whole name on the label before forwarding it.
People have said before, moving is an excellent time to get rid of all the stuff you really don't need that you have been hanging onto!
Good luck!