Depends how big the stuff is. My Dad loves to use the flat rate boxes at the Post Office because he ships stuff that is small but heavy out to his brother in Hawaii. They have a few different size boxes:

https://www.usps.com/ship/priority-mail.htm#flatrate

Try using pirate ship, they offer discounted shipping labels. Usually at least 50% off the retail price, and you can print the label at home.

I ship a ton of stuff and I always check pricing through the 3 big shippers. USPS, UPS, and Fed Ex.

22lbs isn't the only thing we need to know. The size of the box is a huge consideration. Typically USPS is going to be your cheapest bet. Unless you are shipping something very large, then I would go with UPS. FedEx tends to eb the most expensive service for all sizes of shipping in my experience.

Pirateship.com

If the box only have books or media you can do media mail with USPS, or use pirateship like others said.

USPS flat rate, if at all possible. Depends on how big it is. The USPS Region B box is also a screaming deal, and it's sized between the medium and large flat rates. If you go with FedEx or UPS, ship to a commercial address if you can. They both have a residential surcharge, but USPS does not.

we use parcelpath.com exclusively and love it. It is free, and they have the best discounts for UPS and USPS online. Also, they have mobile barcode so any UPS store can print your label for free if you don't have a printer at home.