Making and Maintaining Friends

I recently met a girl who goes to my school while on a flight. We had a decent conversation so before we got off I told her that I didn't know many people at our university and that if she was cool with it I'd like to keep in touch with her. She was nice about it and agreed and told me to contact her after summer as we both will be far from university this break. My question is how do I turn this acquaintance into a friend? My original thought is to just invite her to a comedy show or something. I just don't know if that is a bit much for someone you just met. I guess I could invite her to get coffee so I could get to know her more but I didn't want it to seem like I was trying to actually get with her. There's nothing wrong with dating the same sex I just didn't want to mess up a friendship before it started because she thought I was inviting her on a date and not to stereotype but I think she might be Muslim so I don't want her get freaked out. I haven't really been around people that much but I know I am going to start working soon so I'd like to know if I am over thinking the coffee thing or what I should invite her to do. Any suggestions for this girl or future friends?

*i posted this in the school section first on accident but I think it is best placed here*

Either the comedy show or going for coffee sounds just fine to me. I don't think inviting her to a comedy show is too much at all. It might be dicey depending on the subject matter of the show but overall not too much. Inviting her to coffee will help you get too know her better. Good luck!!!

Thanks!!

Yeah, going out with her somewhere doesn't seem like a bad idea. Lots of people get to know each other that way. Wish you good luck!

Just ask her to go to coffee or somewhere, nothing wrong with that. Don't over think this and wonder if it's "too soon"