As gunstar mentioned, there are a total of eight elements in the game: magic, earth, life, undead, fire, air, water, and tech. The bonus areas usually contains treasure chests (in-game coins) and hats (provides a small bonus to your Skylander). Another thing that each separate Skylander unlock are challenges. Each Skylander has their own short challenge stage, which gives a permanent stat boosts to your Skylander if the challenge is completed (challenges aren't lock to one Skylander; any can attempt it).
But having all the Skylanders isn't necessary. With the starter pack, you already cover magic (Spyro), tech (Trigger Happy), and water (Gill Grunt). Get the pack with Eruptor (fire), Chop Chop (undead), and Bash (earth). Finish off with a life (Stump Smash or Stealth Elf) and air (Sonic Boom or Whirlwind).
However, Skylanders aren't created equal. Some will outshine others by miles right off the bat, while others need some serious in-game coin investment to become decent.
And as for the adventure packs: I'd say save your money at this point. It's $20 for one Skylander + one extra stage + 2 items that's usable in-game. Not as awesome compared to having three new Skylanders. But as gunstar also mentioned, keep an eye out for the adventure packs as they aren't sold separately like Skylanders.