One box source is not mentioned is Priority Mailing Boxes, which are different from regional and flat rate boxes, they are free, but you have to use them with priority mail. All of the priority mailing supplies are free to order on USPS.com but can take a week or two to arrive.
Other good link is the USPS cost estimator, sometimes the regional rate boxes can be cheaper than flat rate or regular Priority (not as often now unfortunately).
If you ever want to know anything about shipping USPS, there is a resource called the Postal Explorer which is the one stop destination for any official rules ect. for the USPS at pe.usps.com
Also, First Class Parcel is under 13 oz not 1lb, at least for retail customers.
You get to learn a lot when you spend years working at a Post Office(well technically not an official Post Office, but RSSBP, but we often have more volume than the actual post offices around here so.)
Also, thank you for mentioning the cost savings of Flat Rate boxes, the medium and large ones are only worth it for cross country packages that weigh 5-10 plus pounds. So many people just use flat rate boxes and end up paying 150%-300% more than the cost of regular Priority.
My favorite USPS boxes are Box 4, Box 7, and the 1096L