What is the best way to send packages from the USA to European countries?

You will find a number of third party services that will offer you discounted USPS shipping including stamps.com, shippingeasy.com, shipstation.com, etc. Note that many of these services are getting bought up by stamps.com, which actually may end up benefiting everyone as they will have more leverage to get better rates from USPS. You'll also be able to get a discount when you use some shopping carts like Shopify.com. Bottom line - shop around and see which one will give you the best rates - the higher the volume, the better the rate!

Heard good things about GoodsCloud (www.goodscloud.com)

If its for sales through Amazon (or even elsewhere) FBAPrep.com is one of the best out there. They can handle importing, preparation (repackaging, barcoding, etc.) and then final shipment. Plus, they know the special requirements of Amazon and other third party marketplaces.

Can you give more information on what your product is? Then we can figure out what you need in it. Sounds like electronics...but what?

Talk with the folks at MyUS.com about your situation. Likely they'll be able to provide a simple + cheap way to handle this. And... overseas shipping is always expensive, so depending on your product, profit margins may not allow selling through overseas Amazon organizations.