The world's leading international shipper is DHL (owned by the German Post Office).
For calculating the rates to display on your shopping cart, you could configure Shopify to use USPS Priority Mail rates plus a small percentage, but call it something like, "Premium International SAhipping". Monitor your shipping profit margin each week, and adjust the shipping rates accordingly.
DHL delivery is very fast (2 to 4 days to most countries as opposed to weeks via USPS), their tracking is awesome, and customers all over the world recognize the name.
This depends on the weight and dimensions of the product, but most of the time USPS stands out among the rest. USPS will almost be the cheapest option unless your package is heavy or there are any special shipments that USPS can't ship. But, as you have mentioned, USPS tracking is slow to update or it doesn't provide tracking at all.
FedEx would be a good option since they are fast and provide excellent tracking info. Also, since you are shipping international, you need to take care of the customs duties as well, which is handled well in FedEx. But, since Shopify doesn't directly handle FedEx shipping unlike USPS, you will have to manually handle this or use an app like FedEx Rates, Labels and Tracking app to handle FedEx shipping.
Niteo : I suggest you to use a combination of carriers to ship international based on the product category and weight. For example, if you are shipping very heavy items which do not have a premium delivery, opting for USPS Priority International makes sense as they have the cheapest rates and you are sure the order will be delivered(even though a little late sometimes :)) . If you have certain items that need to go premium(3-4 days), you can opt for either UPS, FEdEx or DHL. Most of the premium services have similar prices so ultimately it depends on your preference and also certain special aspects that the courier provides like dry ice shipping, hazardous goods shipping, etc. If you are looking to ship using multiple carriers, you can use the Multi Carrier Shipping label app for this purpose.