Good choice with the Nikon !!
With regard to the D60 vs D80.. .. I would actually recommend the D60 instead of the D80. for the following reasons.
1) Its cheaper.. its got the same number of MP
2) Its newer technology than the D80. The processor and software in the camera is better. eg :- It has Active D-Lighting which brings out more detail in the dark and bright areas . better colour etc. and better at High ISO compared to the D80.
3) Its lighter.
4) It works with all the new lenses that you would be getting( on a budget..)
5) it has all the basic functionality if you need it.
6) Its designed to be a transition camera for a person who is used to a P&S camera. with all the nice presets etc. if you have used SLR (film) cameras before then the D80/D90 would be the better choice.
7) The D60 has a better LCD.
There are a few other reasons I think but I cant think of them now
With regard to the lens. Although the SLR is designed to heve interchangeable lenses .. I would suggest that if you are new to it. You should get one lens to start with, with a good range, so you don't have to be frustrated with changing lenses so often.
My suggestion for a lens with your D60 would be the new 18-105 VR.
You can build a nice system around this base, I think. Everyone is different but this set up should cover almost all kinds of photography. Once you have played with this for half a year to a year or so. You will be able to gauge your own personal directions. Some guys here would be using a 100-400 lens 80% of the time, others would be using the 24-70, and still others love the 10-20 sigma. I myself could happily take lots photos with only my prime macro 150mm f2.8 sigma.
Since you are just starting. I would like to suggest that a simple generic setup would be best till you find your "view" of the world.
Hope this helps..
Oh PS: The money you save between the D80 and D60..... spend it on a good tripod (most underestimated equipment of a new SLR user) and a flash, like the SB600 or SB800 if you can get it cheap. One of the key advantages of the Nikon system is the excellent Flash capability, worth switching systems just for that
(You hear that canonites )