Consider the Little Box of Magic Tricks from Barron’s. I’ve seen the Ideal 100-Trick Spectacular Magic Show Suitcase well spoken-of. Consider too Joshua Jay’s The Complete Magician Kit. The Klutz Book of Magic includes props and can be considered a magic set all by itself.
In my opinion, the best magic sets are ones you make yourself. Hand assembled with love. You know your own child the best.
Props: a set of cups and balls (you know your budget best — these range from inexpensive plastic ones (and some big-name pros use the three-color inexpensive ones in their pro acts; e.g. David Regal) up to OMG three-figure prices.
A ball vase. Everyone loves a ball vase, especially someone who is going to grow up to be a magician. Check the number of pros whose first trick was a ball vase, given to them by a dad or uncle at age six. Just because it’s an inexpensive plastic thing that comes in every kiddie magic set doesn’t mean it isn’t good. Ed Marlo had a ball vase routine. I do Michael Skinner’s ball vase routine (which involves appearances, vanishes, penetrations, color changes, and ends with the ball vase in the spectator’s hands and examinable).
A set of 4″ or 5″ linking rings.
A set of 1″ sponge balls.
All of these are standard dealer items and available at any magic shop.
Ordinary coins and cards you can procure locally and as-needed.
More books: consider Gotcha!: 18 Amazing Ways to Freak Out Your Friends by David Acer. There’s a book, and matching DVD, called Wild About Harry by Rachel Colombini which features Harry-Potter-themed magic tricks. The tricks vary in skill level, but nothing a sufficiently motivated young magician can’t master (e.g. a book test that proves beyond the shadow of a doubt that you’ve memorized the entirety of one of the Harry Potter volumes).
Also for the young … Google on How To Make a Harry Potter Magic Wand to get a huge selection of instructional pages and videos (an excellent parent-and-child craft project opportunity). An awful lot of magic involves arts-and-crafts. This may be your first; it won’t be your last.
No matter what you do, download and read Under/Over by Joshua Jay from Vanishing Inc. It’s a free ebook (PDF format).
Find or make a nice wooden case that will fit everything, and there you go.