What Taxes Should I Charge??

Hello!

I'm having the worst time figuring out what kind of sales tax I should be charging my customers. In Commerce > Taxes, there's the ability to charge both the "state rate" and the "zip code rate". Should I charge both rates or just one? Is it different per state? I've attached an image to show what I mean. 

If I charge both the state and zip code rates, do I need to manually enter the tax rate for every zip code in the U.S. and Puerto Rico?  

My business is based in WA and we'll be sending products across the country (and possibly internationally). 

Additionally, should I charge taxes on shipping? I didn't even know that was a thing. 

Thanks!