She's adorable - congratulations on your puppy.
As far as the back yard is concerned, personally I would never be comfortable letting a dog run loose in an unfenced yard, even if they are perfectly well-trained to come when called. There is just so much that can happen, and even a dog with a completely reliable recall in all other situations can and will go after something if it is interesting enough.
A young puppy who's exploring her world and will probably start testing to see what she can get away with once she gets a bit older seems very much like tempting fate. Sure, you can work with her on staying within the yard boundaries, but the safest way of letting her outside will be to be with her and keep her on a lightweight long line, such as a cotton tracking line or even cotton laundry line (provided it has a good handle on your end so you don't end up with rope burn).
I also agree with the poster before me that it will probably be quite confusing to her when you walk outside the property. On one hand, you're trying to teach her to stay in one area, but on the other hand you're telling her it's okay to go out of it. Very confusing, especially for a little one.
I'd just start putting a leash on her and walking her off the property, and consider getting some sort of fencing so that she can be in the yard safely. Even livestock / kennel fence (the kind that is large rectangles or wire) is a better solution than just leaving her loose in an unfenced yard, especially so young.
Training starts the second you bring a dog home, regardless of their age. Just keep sessions short and fun.
And like the posters before me, I have to echo the sentiment about the choke chain. Like any kind of training collar, they should not stay on the dog all day long. If you have to leave a collar on your dog all day, make sure it's a well-fitting flat nylon or leather collar that has your information (phone number, etc.) attached to it.
Use the training collar only when you're actually training, and only when the dog is really old enough to have a need for a training collar. I don't think a choke or a prong should be on a dog before at least 6 to 9 months of age. At your pup's age, a flat nylon collar should be sufficient. If she's quite a handful, a nylon martingale is the next one to try.
