What from the original game is compatible with the new game?

I can confirm that the Adventure Pack levels are in the game, and they are exactly the same.
With the exception that the Soul Gem for the particular character is missing.

All the items work as well.

All of the old Skylanders themselves also work (I personally have 18).
The only thing you need to do is claim ownership of them (under the character menu).

Note: Heroic Challenges power-ups are NOT transferred over.
All the old characters can go up to level 15.
You can take the hat you are wearing, but it does not count towards the hat total.

Really the only reason to get the new figures is to get the new rewards.
You really only need one giant & one of each element to find everything.

As soon as I claimed ownership of Spyro, Gill Grunt & Trigger Happy it gives you an Exp. Bonus.
The Tree Rex figure also gives you an Exp. Bonus since it's apparently not a starter Skylander.

So unless you just like certain characters (in the new figures), you really don't have to buy anything after the "Portal Owner" version (which comes with Tree Rex & the game).
Of course if you want the new Cynder & Jet-Vac then grab the Starter version.
BTW Walmart had a Glow in the Dark version of Cynder in the Starter version.