You can initiate conversation with a girl without seeming needy by simply approaching it in the same way that you would when talking to a friend.
Instead of trying to impress her by saying something that is designed to get a favorable reaction out of her, try to be more natural.
Try not to look at her as some girl that you are trying to get.
Instead, just talk to her in a way that makes her feel as though she has spoken to you before.
An easy way to initiate conversation would be to use your environment.
Simply pick something out in the environment that you are in and start talking about it.
Perhaps it is a store, video, music that is playing, etc.
Use that as your first topic.
Oftentimes, further conversation will flow from this point on, as long as the both of you are talking to each other with ease.