Nikon 50mm 1.8D on d7000?

I've decided to save some money and go with the Nikon d7000 instead of canon 7d.

just making sure, will the 50mm 1.8D instead of 1.8G work on the d7000?

The 1.8G is a lot more money as I heard it focuses more quickly, but I also heard that the 1.8D will work perfectly on the d7000…

Am I correct?

You are correct.

ANY Nikkor AF, AF-I or AF-S lens will auto-focus on the D7000

In addition, if you do not mind manually focusing the lens, ANY Nikkor AI or AI-S lens can be used. You focus them using the electronic rangefinder in the D7000 viewfinder.