The Extreme cards are Class 10. The Extreme III are different - I believe they are class 6 since they were released in 2005. There is also an Extreme IV that is the successor to the Extreme III and I believe it is also Class 6. The Ultra cards replaced the Extreme IV.
The Sandisk site says the Extreme (Class 10) and Ultra SD cards are compatible with the D7000. It does not mention other cards. The manual for the D7000 will likely have some specifications for approved cards.
With other manufacturers you will see reference to both maximum and minimum speeds. The 30mb/second is a minimum speed for both read and write - it equates to a 200x rating which is the maximum speed - typically for reading which is faster than writing.
The big difference in these cards is read and write speed. I've used a large card with slow write speed in the past and it can really slow down burst shooting and downloads. I would be concerned about shooting HD video with a slower card.
I don't see any reason to only go with Sandisk, but I would go with a known brand. You so need to watch the speed on various cards as there are a lot of discontinued products on the market. I did some research yesterday and was able to find Class 4, Class 6, and Class 10 cards all available as new.
I just purchased 2 16gb Sandisk Extreme cards for the D7000 I ordered. They are about $90 each. There is a rebate available from Sandisk, but limited to authorized dealers. Other dealers like Amazon fulfilled seem to be discounting the rebate from the price.