I live in the midwest. I have done shipping for items on Ebay for years so I do understand USPS shipping...I got pretty good at sorting through the USPS site, all the info, prices and comparing all the options available.
If you live outside of the east coast zone for the APO, use a FRB. Once you get past about 5 pounds and the box gets bigger, the price goes up substantially.
There are three sizes of flat rate boxes. The small that fits very little for $4.95 or $4.80 online, the medium comes in 2 shapes. These cost $10.35 or $9.85 if you purchase the postage online. There is a large flat rate box that normally costs about $13.95. You get a $2 discount shipping to an APO and it costs $11.95, $11.50 if you buy it online. Delivery confirmation is also free online. You will pay extra at the post office for delivery confirmation. The post office will ship you the boxes in quantities of 10 for free. Since the APO is considered a domestic address, you can put up to 70 pounds in the box for the same price.
You can also fill out the customs form for the APO, AE online. It will come up automatically and ask you if you wish to fill out online and print. VERY easy. The directions for the form are there and easy to follow.
An example, I just packed an 18 pound, large flat rate box with an APO address. From my zip code, it would have cost about $28 to ship the same box without flat rate shipping... I paid $11.50 online...HUGE difference!! It arrived 5 days later at the APO.
Also, you can request free carrier pickup from your home for your packages as long as at least one of them is a priority box. I have done this numerous times. It works great.
Hope this helps!!