The answers are really your own to answer. You said you still have your own personal problems you want to work out. Depression and the break up with your ex. If you feel that these issues would hurt your relationship with the new girl, then deal with them first before you try something with her. You are not being selfish, you're being smart. If you think you can handle those emotions plus all of the things that come with a new relationship, then by all means try something out with her. Just don't overload yourself, depression and a break up are a lot to deal with, I'm going through the same at the moment. I personally wouldn't be ready for another relationship just yet, still sorting out too much in my head to start thinking about someone new.

It's all about what YOU feel that YOU are ready for. If you're not selfish for yourself, who will be? She's not gonna fall off the face of the earth if you feel that you need some more time.