First: If you want the Kaos Trap, the way to be sure to get it is to buy the Winter Bundle pack if you can find it. At about $100 retail, it's a bit of a bite to take, especially if you've already spent for the "Starter Pack".
This is not a review of the game play. In my opinion, it's really fun, and I like the physical interface with the game.
What I didn't know:
Elements: As you progress through the game, you'll be encountering certain areas where bonuses apply to attacks by Skylanders that match the battle zone element, or "trapped" Villains.
Traps: These retail for about $6 each. Your starter pack likely comes with one Water Trap and one Life Trap. When you defeat a Villain, and you have a trap that matches the element of the Villain, you may temporarily use that Villain to do battle. If you complete the Villain's quest (the Villain must be trapped), the villain changes color and acquires a new attack/ability. Each trap can hold one villain at a time. Some strategies might be useful to swap between villains of the same element, so multiple traps of the same element may be desired. Most of the traps support swapping between 3-6 villains within the same element (one element per trap, one villain at a time per trap). Only when you're at the home stage, can you swap out villains within an element (the exception being an opportunity to swap a newly captured Villain within a currently occupied trap).
Trap Masters: These retail for about $16 each and they are the only way to unlock certain areas with matching elements.
Skylanders: These retail for about $10 each and each have its own attacks/abilities and element. These cannot open the locked areas, but they are useful for different attack reasons, including being the only practical way of continuing a battle as an "extra life".
Availability of pieces:
You'll find out that some traps in particular are harder to find at the store than others. At a local Wal-Mart, I found a bunch of water and life, some magic, a couple each of fire, earth, and tech, and no air. Also, no dark or undead unless purchased in the set. Certainly, no Kaos Trap on its own, but it was included in the Holiday Bundle.
Likewise, a similarly sparse number of Trap Masters: Tech, Air, Fire, Water were available as stand alone, while Dark and Undead were available as add-ons (bundles).
How much money will you eventually need to spend?
It depends on if you want to be able to complete all goals or just play. There is plenty to do without needing to spend beyond the starter pack. Certain areas and quests just won't be able to be accomplished without the tools to unlock the quest or areas. The figures are very cool to play with and look at and are cross-platform between consoles. The character stats apply to the specific figure in use, so two of the same figures will have different stats.