Hi Rolexer,
My business ship stuff all the time with express courier companies to Europe, US, Australia.
I assume that cost is not an issue since it's a high value item and with reliability, security being top priority. In which case, I would ship with the "big boys" like DHL, FEDEX, or TNT.
From my experience, TNT offers the best rates. However, this is coming from the perspective of a corporate account where I enjoy good corporate rates.
If you have a trusted friend that does a lot of express courier shipping like me, with a corporate account, I will suggest you "leverage" on his rates and ship using his account.
As for the packaging, invest in a good solid materials that you should be able to source easily. Your watch box should be placed inside another solid box for protection. Take note that the packaging will be travelling half way across the globe and exposed to various climate change and potentially high humidity/condensation can occur.
However, you want to keep the box as small as possible (without compromise to protection) because the size of the package will affect the overall courier charges.
Cheers and all the best!
BTW - why did you sell to the States? Was it better price?