Lot666 said: "I'd just like to offer some general stage door etiquette suggestions, if I may.
Most performers are very gracious and patient, but please be polite and unassuming in your interactions with them. When they sign your Playbill, thank them. Also, ask before you try to take a selfie; almost all (with the exception of some Hollywood types) will smile and say "Of course!", but put yourself in their place and afford them the same courtesy you'd like the public to show you.
Many people are fans of certain performers whom they consider heartthrobs, and there's nothing wrong with that, but these people are also artists and that's what most of them want to be appreciated for. If you really want a picture with someone like Mr. Karimloo, he will likely be happier to hear you comment on his performance or his voice rather than his eyes or his biceps. 
Echoing all that's been said, but especially this. The Anastasia stage door is generally very friendly, even if a bit crowded, but a little politeness goes a long way. I ended up in front of/next to a group of very... enthusiastic teenage girls, whose reaction to Derek appearing was to loudly shriek (right in my ear) and squeal to each other about him as if he wasn't right there. He was polite as could be, but spent considerably more time chatting with my mother and I and with the group on our other side. Talk to them like people, ask a question about the show or a past show of theirs or something, and you can't go wrong! And same goes for the ensemble too - they don't always get asked to sign, but they're often some of the nicest and chattiest people! Hope you all have a wonderful experience!