What's the best way to ship internationally?

Site URL: https://www.filipinofoodcrawl.com/

Hi, I'm a seller in the US and I would like to be able to offer worldwide shipping. However, I don't know what's the best way to calculate the shipping cost so that a customer can settle the shipping fee at checkout. Right now, if a customer would like their items shipped abroad, I charge a flat rate fee but sometimes the flat rate is either too expensive or too cheap (therefore the customer overpays or I would shoulder the difference) for the item they ordered. Another workaround I have done is to email the customer the shipping fee and they pay the exact amount direct to me, not through the site. While this method of emailing the customer has worked, it is rather time consuming and high touch. 

I currently use PirateShip to order my labels. I have recently discovered the Shippo extension and I'm glad I can now use UPS, DHL, etc. as shipping options, not just USPS. My questions are:

1. What's the best way to automatically calculate the shipping cost at checkout? I know I can calculate by weight but how would I account for the different destinations and therefore different prices?

2. What have others done to set up their shop to ship globally? What shipping software do you use?

Hello, what did you do in the end? Facing a similar issue. Using DHL to ship from UAE and looking at integrating Aftership, Order Desk or Shippo. Any advice would be greatly appreciated.

Please see my reply to your post here: