Congrats! Though I'm curious to know what you mean by "real" startup. What's a fake one?

One of the most important questions to ask is how they're funded. Most startups fail, and funding is the most accurate proxy for stability. At the very least you'll know if it'll be around long enough for you to learn something while working there.

Also, if you're getting stock options, I suggest you read this article (tells you what questions to ask so that you understand what they're worth):

http://blog.alexmaccaw.com/an-engineers-guide-to-stock-optio...