A wizard affinity? I'm honestly not sure what I was thinking when I said that, but I'd say any wizard type familiar would be sufficient as well as any of the elements. Wizard would actually be somewhat unique in that it wouldn't be so good at the transforming, but would have better than average magic abilities, specifically in how much power, not how much skill. You'll see what I mean down below.
Speaking of which, I need to explain what I decided about that don't I? *sigh* here goes...
Why there isn't much magic in this universe (out of game reason)...
Okay, because everyone can turn into different stuff, that's a pretty majorly powerful and useful ability. So in order to balance this out, I'm making magic itself pretty low. This means no spell slinging with fireballs, transfiguring other people, flying, etc. Of course since you can just turn into a fire elemental or something with wings, this really won't be a problem for most people.
How what magic exists works and why it's so difficult (in game reason)...
Anyway, magic will essentially be on a hedgewitch level, make something glow, light a fire, make something small float or invisible, stuff like that. It is possible to get more complicated stuff like fireballs or ground shakes or whatever, but it's like.... a song. Assuming you have enough power to do so, casting a spell is like thinking a song. The easier the spell is, the easier the song is and you can hold it in your head without much trouble. But the harder the spell gets, the longer and more complex the song becomes until you can no longer hold the whole thing in your head at a time for the duration of the song. If you're lucky the spell just fizzles out. If you're not lucky, part of it will take effect and it will pour out of control in a sort of whiplash. So basically the result is that harder spells take a lot of focus for a lengthy amount of time. Calling a thunderstorm would be like conducting a symphony in your head single-handedly. This isn't really something you can improve at much like you can with transformations so what you start with is what you get. Even if you are somehow really good, it usually takes too long to cast most spells to be useful.
So that's how magic is hard. This is how it's easy...
Right, because magic is low and technology is also pretty low, and I like things to be cool, this is where magitech comes in. People who are better at magic that usual tend to go into business as mage-smiths. They go through that whole difficult process of setting up the spell and then they tie it into something. Maybe it's a crystal, maybe it's related to the spell, maybe it's something else entirely, but the net result is something that has the spell permanently tied into it which can be used over and over without having to deal with casting it each time. Now when you normally cast it, you power it from yourself, but these artifacts don't generate energy the way people do so they instead draw off ambient energy in the environment.
Powering spells
Okay, usually people naturally generate excess energy (exception being when they're sick or injured and need the extra energy for themselves). This is generally called a person's aura and tends to extend an arms length away before dissipating. And before anyone asks, no this is not generally visible to people. Anyway, in places where a lot of people live, this sorta saturates the air and no longer just dissipates. So after a while places where people live acquire their own aura. Artifacts feed off of this and charge themselves so that they're usable. While creating this I realized that it's very similar to the lux system found in Tales of the Questor. I haven't actually come up with a name for this energy, but let's call it 'aura' for the meanwhile.
Notes on transportation
Since there's no gravity just about anything can travel from one island to another. The only things to consider are maneuverability, propulsion, and ability to not crash land. The first two issues are solves by any number of things including paddles, fans, etc. The last issue is generally solved with engines being made with chunks of islands in them. This establishes an artificial gravity throughout the ship and has the bonus that when it suddenly enters a gravity field it doesn't crash but rather continues to float. In order to not clutter, ships are generally docked under an island. In order to leave, the engine is turned upside down momentarily so that the bottom gravity of the island thrusts it away aided by the ship's own 'lift'. (this is why people should probably strap in or hold onto something during taking off)
Notes on flora and fauna
In a world where everyone can transform, how does this effect the animals? Well generally animals have a much more limited transformative ability with a pretty specialized affinity on their species. Basically this means a cat will always be a cat but it can grow fins or wings, enlargen ears for heat venting, etc in order to undergo quick adaption to a new environment. This means that any species can go just about anywhere they want, though they'll be recognizable as the same species usually. You'll find schools of fish flying through the air, foxes in every environment imaginable, and even cats that swim! Okay, maybe not that last one... cats hate water no mater what tweaks are made to them...
Ecosystems can exist in a few different ways. You're all familiar with how it (likely) works in a gravity setting, but they pop up in between islands too. When clouds of water form but don't actually dump anywhere, seeds will sometimes be caught in them and start to grow. Once the plants start growing, small herbavores come in and the system grows similarly. After a while you end up with these floating jungles that just wander around. It is theorized that if such a jungle exists long enough it will turn into an island of its own, but there are no records of this actually happening.