If an investor and a founder sign a contract, could they use a neutral country with an appropriate legal system for governing law?

The contract is governed by the state in which the "Subject" of the contract will operate

If the Subject should change operating location then the governing body changes. This applies to state laws of course, but not federal laws for obvious reasons.

I would make the contract relevant in the country wherein the the company is incorporated. It will allow you to use the same legal team to resolve any of the issues. You should also only be using one of the "big 5" firms: Greenberg, Cooley, Sonsini, Gunderson etc. They usually have representative offices in most of these countries and you get the efficiency of keeping everything under one roof.

There are many other efficiencies of using these large firms that already service most VCs, funds, startups. They understand the ecosystem, work well together and can give way to strategic business introductions (investment, partnership, acquisition).

While governing law is important, venue – i.e., where a lawsuit must be filed – is even more important tactically if a dispute arises.
If there is a great disparity in negotiating power between the parties, the one with the greater power is likely to prevail on this issue (and many others).
If a compromise is desired, choose a neutral country (with an appropriate legal system) for governing law and venue.
An approach that will reduce the likelihood of a lawsuit being filed: If one party initiates a legal action, it must be filed in the other party’s country, and that country’s law will govern.

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