First, you will want to get the USPS Version: 2015-05-31 K7 add-on for your site:
Version: 2015-05-31 K7

Load that USPS shipping module to your server

Next, create the US 50 States + DC Zone definition ... that link I posted will give you a fast way to set it up without having to build it 1 state at a time ...

Next, once USPS is done, we can move on to what you want to use for the International ...

I am not quite sure why you said you have Per Unit perweightunit and Zone Rates zones installed, unless it is because you did not know you needed to grab the USPS module and now are stuck on what to do next ...

I suspect you might want to see if USPS handles all of your shipping needs for both Domestic and International before adding the Zone to it for just the US 50 States + DC ...