When you are dealing with a mix, it is really hard to say which characteristics will be inherited. As you have met her, and nothing appears to stand out as worrisome, then you should be just fine.
I am a bit concerned that at 4 months, this puppy has had no shots. While I don't believe in over vaccinating, I do think that the puppy basics are very important.
Large, open spaces are wonderful, but if they are not fenced in, your new puppy should only go out on a leash. As this is your first dog, I strongly suggest you find yourself a good trainer, that teaches using positive methods, to attend classes with. A good trainer will teach you so much more than just some basic commands and set both you and your puppy up to succeed in life.
Whether or not your puppy is going to depend very much on you! If you attend classes, train and socialize your puppy - you should have a wonderful dog! Equally important is remembering that young children need to learn how to treat dogs as well. Hitting, pulling and poking are things that we do not do to our dogs. Your pup needs to be left alone at meal time and any time she has a high value treat, such as a bone.