I haven't played any of them, but my son played all three and based on a lot of conversations with cognoscenti I'll offer this:
Pokemon is a decent CCG for kids. There's some strategy, but it's not too deep. You can play and enjoy it without going broke. At some point the kid in question will probably want to move on the MtG. The show is decently written for a kids' animated show. The Pokemon characters, card game, video game and show work together pretty well. While the "cock fighting with teddy bears" assessment is pretty accurate, the values in the mythology are otherwise reasonable.
Yugioh is a souped up game of war – cards with higher numbers win. There's not a lot of strategy. The show is a bald-faced commercial for more cards. The kids will always want more cards. You will spend a lot of money on cards. The show is stupid. They representation of Egyptian mythology is pathetic and the rest of the Yugioh world is pretty crass.
Magic is apparently a pretty decent game. A lot of gamers I respect, who play other games and know what their choices are, play Magic a lot. You can spend as much money as you want on cards, but if you only spend a reasonable amount you can still have fun. it can get *very* complicated when masters play certain combinations, and the official rulebook is a nearly inscrutable legal document. This is (probably) necessary for the intense tournament play. But if you read and use the rules that come with the starter sets you won't have a problem playing for fun. Interrupts, follow-on triggers, the "stack", etc are all there for the experts, but you can play the game without worrying about those.
So I would steer a kid toward Pokemon if they're younger and the TV show component is important. I would work hard to keep a kid away from Yugioh. On the other hand, some parents and kids have had a not too traumatic experience with Yugioh, and if all their friends are playing that you may get sucked in. Spending time and money on a stupid show and game may be an acceptable price to pay if you kid gets to be part of an active, fun, and otherwise wholesome social group.
Handing a young girl the rules to Squad Leader and explaining "this is a real game" won't work. Or at least it hasn't yet.
I would definitely not say Yugioh is on a spectrum between Pokemon and Magic. The spectrum would go War – Yugioh – lots of second rate games – Pokemon – lots of fair games – Magic.
I know nothing about the Yugioh dice game, but would refer you to boardgamegeek.com for all the info on all the boardgames you could ever want.