Prestashop is a dead duck as it doesn't support true multi-currency (ie: payment in the displayed forex currency) but just shows what it might cost based on an exchange rate. Doesn't help that the modules available get slated for their support so no joy there.
Magento just got a big no from BabyReflux and having spent some time trying to understand it, the update process really put me off...
BigCommerce... LOL... Do you need to ask?

Shopify
Not self-hosted and doesn't support single stores with multi-currency. Also has a frustrating monthly app cost for most add-ons which adds to the price... Throw in Stripe as the primary payment processor and extra costs for using an external processor I'm not too keen.. That said it's ticking a few small boxes so may become a test site sometime soon just to kick the tyres.
All in all, it's going to be a long, painful process...
