International shipping problem

Hi all, I’m at a total loss with a woocommerce requirement. I’ve created this shop https://london-gothic.co.uk/shoppe/. Initially we were only shipping to the UK which works fine but now we are looking at branching out to specific destinations abroad: Europe, USA, Asia, Australia and New Zealand. I’ve added those shipping zones of course.
My client has specific costs per product for each of those zones e.g. Europe T-shirt is £8, Europe artwork is £30 etc. it’s different for each shipping zone.
How do I set this up please? I can’t believe it’s not very straightforward, why does it seem to be so complex? I’ve tried about three different plugins but so far with little success.
Please, can someone help me or guide me to someone that can?
Sean