Q: Should I list my position or the company I work for first on my resume?
A: Position first, Company second.
Like so many resume “guidelines,” that is not set in stone. However, it's the approach I recommend because while your employers are important, they do not say as much about your qualifications as your role in that company does.
Tell potential employers first what you do/did, then you can tell them who you do/did it for. You're marketing yourself, not your previous employers.