The first thing you need to know is that the TCG is split up into formats. Currently there are three major formats. There is Standard, which is XY-on. There is Expanded, which is BW-on. And there is Unlimited, which allows the use of nearly every card in the game. Multiple times a year there will be new sets released called "Expansions". These add around 100 to 150 cards to the already extensive card pool. Some set name examples are Black & White Boundaries Crossed, X&Y Phantom Forces and X&Y Base Set. You can find more expansions and details on them
here. Also,
here is an official list of the legal expansions usable in each format, which provides more details on the Standard and Expanded format.
You also mentioned EXs. EXs are a special mechanic that can be seen through Black and White (BW) and X&Y (XY) sets. EXs are more powerful and rarer Pokemon that have high HP and when defeated, give up
two prize cards. There are also a few other mechanics like BREAK, but I suggest you read the Appendixes of the current rulebook found online
here.
You also mentioned something about illegal//legal cards. So you know, the TCG has a ban list that prevents certain cards from being used. In the Expanded and Standard format, only
Shiftry NXD and
Lysandre's Trump Card have banned. Don't worry about any cards you obtain getting banned - cards getting banned is extremely rare in Pokemon TCG.
Okay, time to get to what this mysterious Power Beyond Tin is. These tins are something like expansions to your card collection, providing a guaranteed EX (Hoopa-EX in your case), as well as four booster packs. Booster packs will contain 10 random cards from a certain expansion that can add to your gameplay. The Power Tins are not designed to be make a full deck, instead to boost your collection. You can also by single booster packs like the ones in the tin that expanded your collection and can be nice stocking stuffers.
It is recommended to obtain a Theme Deck - a pre-constructed 60-card deck - to start playing Pokemon with. Each Expansion will have two pre-constructed decks of the Expansion's cards available in stores. Each Theme Deck comes with 18 energy split between two types, about 10-15 trainers and ~30 Pokemon. These also come with a coin, damage counters, a themed deck box and a themed two-player mat.
It is best for you to choose a deck that features two types that your nephew likes, or is of similar type to the cards you obtained through the Power Tin. You may like to list all the cards that your nephew has in this thread so I can recommend the best Theme Deck for his cards. Also some of the more powerful theme decks in the X&Y format is the Dark Hammer deck and then the Resilient Life and Destruction Rush decks. Best thing is, you can always stuff a Theme Deck in a stocking if you so wish! :>
As a Theme Deck contains just 60 cards, you'll need to get a second theme deck (generally best to be different to the one you might get for your nephew). There is, however, Battle Arena Decks which contain TWO 60 card decks and also have some of the best cards in the format (unlike Theme Decks). Battle Arenas also contains two coins, two sets of damage counters, two custom deck boxes and a two-player play mat. These Battle Arena are the
Xerneas vs Yveltal Battle Arena and the
Mewtwo vs Darkrai Battle Arena Decks. These will, of course, cost a bit extra, and can be difficult to find, but they are really worth your money and is my first recommendation for both old and new players.
Anyways, I hope that wasn't a too hard read! If you have any more questions, feel free to ask! You may also like to read up on the
TCG Resources that the PB TCG Team has created, which may be further helpful in your TCG endeavors.
