What lens for a Nikon d5000 should you choose?

With few exceptions, you're going to be much better off only buying Nikkor lenses. Stay away from Sigma and Tamron. The D5000 doesn't have a focus motor, so only buy lenses AF-S, AF-I, or G lenses if you want auto focus.

I'll assume you already have the mediocre kit lens (18-55mm). Next you should invest in a fast prime. The Nikkor 35mm f/1.8G AF-S or the Nikkor 50mm f/1.8G AF-S are both Excellent lenses.