What lenses would be the best for birding?

There are some better options, but they come at a price.

Professional wildlife photographers generally have a 400 mm f/2.8 (over $7,000) and a 600 mm f/4 (nearly $8,000). They can invest this kind of money because they are part of their set of tools.

You need to remember that the best lenses for your D60 are Nikon AF-S (super fast auto-focusing)

As far as the “380mm” lens goes, there is no such lens. What it may be is the 35 mm equivalent of a 210 mm is 380 mm on your camera.

The Nikon AF-S 70-300 mm VR would be a 105-450 mm, plenty to get you started shooting birds.

If you look at the 70-300 mm lenses made by Sigma and Tamron, you will see that they do not have any image stabilization (VR or IS). If camera movement is not going to be a problem (you will be using a tripod), then you will notice that the Sigma 70-300 mm is $210 and the Tamron 70-300 mm is $170

You will have to ask yourself this. In twenty years will either of the generic lenses still be performing on my newest Nikon body? Will I have to eventually spend the $590 for the Nikon VR lens?

There is a huge difference in cost between the Nikon and generic lenses. I suggest you go into a store that sells both Nikon and either Sigma and Tamron and with them both mounted on your camera, take some test shots and then view them at home on your large computer monitor. The look, feel and resulting images will tell you more than reading opinions here.