I've lived through a situation like this where I founded a company with a co-founder overseas. We had some similarities to your structure in terms of division of labor: sales in the US and development in Europe. We've made it work, but it isn't easy: there's a lot of legal and accounting complexity (cost), and we have had to expend way more energy (cost) in corporate governance, investor communication and financial reporting to make it work.
But the reason reason we did it this way because by having a presence in Europe, we were able to get funding sources and grants within the EU that were looking to create employment opportunities to produce a technology and have a sales footing already established in the target market: the US. I'm not an incorporation expert, but we are incorporated in both countries, with one company being the wholly-owned subsidiary of the parent. I would expect that if you were to follow this approach, the funding will determine what becomes the parent entity - funding determines a lot.
Also, I saw you say "eventually all over the world" and thought "Whoah!!" One market at a time. Localization is far more than language: it's about the market requirements in each target market and unless your product is something universal you have to know the market well to assess fit and make it work in a particular country.
Say you're funded out of Canada. Canadian interests are going to want to see traction in ways they can trust, and that may steer resources away from your target market, which is in California.
Again, I can only share my experience: If incorporating in two countries make sure you have a really, really compelling reason to do so. I have no experience with not-for-profits, so I have no input for you there.
As another poster said, the key is focus early on. I don't know what stage of product/business-readiness you're at, but focus on what's going to get you traction and have an org structure that suits that first if you want to get off the ground.