I am trying to set "no shipping" to orders lower than $50 for certain countries.
Which means we do not ship to country X if the order is lower than $50
How do I set this?
There isn't something like that out-of-the-box.
Maybe using the module from WebShopApps MatrixRates you can try to simulate that rule using prive vs. destination calculation.
I've found some free and paid extensions on Connect: https://www.magentocommerce.com/magento-connect/catalogsearch/result/?q=shipping+restriction&pl=0
I can't recommend but you have some options there. If not, you'll need to code your own solution.
You can also try this extension https://www.magentocommerce.com/magento-connect/shipping-table-rates-by-amasty.html
It will help you to create the shipping rates you need.