Some thoughts:
In YuGiOh, the card-players are limited in what they themselves can do and summon, if I remember the rules of the game correctly by some kind of power-point system. Lets look at spell-points or Ki as a model already in D&D.
We can then select a series of animal-companion type monsters already available to other classes as things you could "cast" based on your level and the number of points you have available. If the creature dies in combat, you lose the ability to summon it for 24 hours.
Basing off the show where the characters usually have goofy catch-phrases do funny movements with their arms and of course, need the cards, we can treat summoning as having a Vocal, Somatic and Material component (the latter being refunded when your creature dies). We can add on to that a "spellbook" ie: the armband type thingy that holds your cards and allows you to play them.
You'd end up being something between the Conjuration and Illusion schools in the Wizard class. I think you could probably do everything you want
with the Wizard class as it is.
I suggest taking a look at the Summoner
http://www.d20pfsrd.com/classes/base-classes/summoner from Pathfinder as a possible idea to work with. It's basically a wizard with a special pet that can appear as human or inhuman as you want, though you can't change its looks on the fly.
I agree with the other posters that this is going to require a LOT of work and I suggest you give a Conjuration/Illusion specialist Wizard a shot.