RE: Getting into PTCG, which booster box to buy?
There's a lot of ways to get into the game, but if you're looking to get somewhere competitively, a booster box is not the way to go.
I'm not going to recommend any particular decks, both because it's hard to know what you will like, and also because the upcoming rotation (in August, which will be Boundaries Crossed-On). What I
will recommend is looking in the
Deck Garage forum. From there, you'll want to just look at the various archetypes and strategies and see what sounds interesting to you.
Once you've selected some decklist or overall strategy that sounds fun or interesting, you can test it on an online simulator such as PTCGO (the official simulator which requires you to acquire the cards yourself, either by trading purchased codes and cards, or by opening packs yourself), PlayTCG (a free simulator with a manual interface that lets you use whatever cards you like; my personal favorite), or TCGOne (another free simulator with automatic play, but is slightly incomplete in terms of cards available). You can use these to play against random online opponents, or to play between each other.
If you're just going to be playing with your children, which is fine (fun should always come first in games), you don't need to stress out about finding something competitive or really strong. Just something with a cool strategy to it that will be more entertaining to play than a theme deck.
After doing some initial playtesting to gauge a deck, you can either choose another or start to build the deck in real life (or you could print out the deck and put the cut paper into sleeves with random cards; this is called a proxy deck and is perfectly legal for casual play at leagues so long as you inform your opponent). Beware that
many competitive decks can cost upwards of $150 USD to build from scratch. That doesn't mean you need to spend so much. Unless you're going to enter a tournament, don't be afraid to substitute expensive cards for cheaper alternatives, or different cards altogether (experiment!).
Good luck!