Working for a US startup from Europe

I just agreed to start working for a US startup, but I live in Europe.

The startup is still small and I am the first hire out of the USA.

We trust each other and want to do this in a clear way, so neither of us has problems with the country we live in ( I am in Netherlands ).

So, I would like to hear some suggestions on what the employement status should be and if there are any contract templates, I would love to see them.

Am I an employee or a contractor? How is that defined in the US law?

(We agreed that I will work full-time for the company, and we don't have a set length for the contract)

I am asking here, because I guess more people have similar work-relationships and would like to know