Wait and see.

In your case, I'm extremely doubtful that a master's will make any difference whatsoever. And getting one now is premature optimization. Wait until you find yourself trying to get a specific kind of job, but failing, because the jobs are being snapped up by people with advanced degrees. Then get a master's. It only takes a year.

I bet you'll wait a long time before that happens.

And why play the go-back-to-school-for-free card now? It's valuable. Keep it in your pocket for a while. You've been in school recently, at Stanford for god's sake -- you've already got a lot of recent contacts from your school days, and you're already in a startup hub. So, wait. After you spend a few years in industry, and find yourself stuck in a rut, you'll discover that it's wonderful to have a ready-made excuse to take a year off, go back to school, and make a whole new set of friends and professional contacts. You might even have a better idea of what you want to study, and where, and with whom.