Planet13 - 6:09 am on Mar 13, 2012 (gmt 0)
I have found that if it's in-state or a contiguous state, it is cheaper to ship plain priority, but everywhere else, it is cheaper to ship flat rate.
That really boils down to how heavy it is, and how big it is.
Generally, the Small Flat Rate Boxes and the Flat Rate envelope / padded envelope are the cheapest, but don't hold much.
Next up would be Regional Rate Box A, which holds more and they only charge you as if it weighs two pounds, even though you can put something like 14 pounds in it. Can't ship international though, only domestic US. So if you ship close by it is around $5.65 or so, and then I think if you ship fa away (like Hawaii) it is a max of $9.85 or so.
After that I think it is medium flat rate box (around $10.80 or so), then large flat rate box (around $15 or so)
Then of course there is parcel post, which only saves a little bit of money unless the package starts to weigh over about four pounds or so. But parcel post service can be brutal. I've had packages take up to two weeks to get from California to New York.