Technically, just about any Nikon lens can be mounted and used to take photos on either camera, but not very usefully.
The D60 only autofocuses with AF-S lenses and only meters with CPU lenses (AF, AF-D, AF-S, AI-P)
The FM-10 will meter with any lens, but it will only be able to use the minimum aperture on G lenses (Nikon lenses without an aperture ring).
Unfortunately, these two cameras aren't an ideal combination for total lens compatibility between eachother. Nikon makes very few AF-S lenses with an aperture ring, and I think they are all expensive pro lenses.
Also keep in mind that a film camera will have a different field of view at a given focal length than a crop digital camera like the D60.
I suggest using your kit lens and whatever other AF-S lenses you buy for the D60 and picking up a few Series E lenses on
eBay for the FM-10. Series E lenses were Nikon's "economy" brand manual focus lenses that were made with cheaper materials at the time, but they are still better-built than today's most expensive autofocus lenses. You can pick a 50/1.8 E and 28/2.8 E for $30 a piece, and a 100/2.8 E for around $100.
