Welcome to PR.
Yes, with the D60, you will have to use afs lenses to get auto-focus. Non afs lenses will work but have to be manual focus.
Since you have a film Nikon, I would guess you also have some Nikon lenses. Because of that, I would suggest you consider getting a D80. Not totally sure what the price difference would be but I know the D80 price has dropped like a rock since the D90 has come out.
You would then have the use of any of the Nikon lenses you have as the D80 has an internal focus motor.
I think a good zoom would be the 18-200 vr if its in your budget. I got a used one at KEH with an ex+ rating for a couple hundred less than new one. The vr will let you get those shots that you'd need a tripod for otherwise. I've been able to get fairly sharp shots as low as 1/15 if I'm careful and the subject is static.
Edit......just looked at B&H and the D60 body only is going for $446.95 and the D80 for $589.95