I don't think they would bar food, especially is well sealed, plastic bags, etc.

Zip code directory — exact zip code:
https://tools.usps.com/go/ZipLookupAction!input.action

Best package rate/choice calculator — select “Package” (see picture below):
http://postcalc.usps.gov/

Good resource:
http://pe.usps.gov/text/dmm300/Notice123.htm#1118064

You can use any old box, any size, as well as the post office boxes.

Robert