I waited 3 years, yes, 3 years before I allowed The Ex to meet my kids and it still went tits up. He showed his possessive/controlling side once I was pregnant with DD, prior to that I thought his jealousy was due to him loving me so much 
I would say that you have to do what feels right for you, what works for some may not work for others and really, the bottom line is that we never truly know someone until we have been with them for a long time or even lived with them. As I said above, my ex showed his true colours once I was pregnant and living with him and I hadn't rushed into anything.
I would also say Zany, it's not just possessiveness you need to look out for, unexplained moodiness, going silent on you, playing the victim and making plans for the two of you when you are meant to be meeting friends are also other signs of an insecure man. Anything that makes you feel uncomfortable is a red flag, your inner voice will let you know, you just have to make sure you listen to it. If I had listened to mine I could have saved myself years of heartache.
Keep smiling Snape, it can only get better 