What type of agreement do I need to make sure I own my product's code and have full rights to amend and sell the business (incl. the code) later?

I have been working as a Business Entrepreneur and have been working with many of the customers from Europe, North America. While creating a White Label solution, the most important part for the owner is to manage the security for the product as well manage the Quality to be delivered within the expected timeline and budget. While choosing a company, the NDA's would work but with them you can also sign a Proposal, SLA(Service Level Agreement) which helps to bind the contract and source code as your own property. As when it comes to offshore development, my suggestions is to choose a company which has been doing this services since more than 5 years now and have been a part of good success stories whose stories are kept confidential. So with the documents, a formal trust would help you create the platform as your own property with the expected quality.
You can consult your Legal adviser in the matter and hope they would align the strategy.

Most international contracts simply require the contract to be legally valid under the jurisdiction of the 2 parties residing countries. This makes things difficult because everything becomes interdependent, and some countries are near impossible to enforce even iron clad contracts. More than likely you will need a lawyer in each country you plan to do business trained in international law. This is about the extent of what I know about international law but you are welcome to contact me as I can usually dig up more information as needed