Assuming that your GF stays with a D5000 body it is recommended to get a good stabilized DX zoom, e.g. a Nikon 18-55 VR or the best in terms of quality the Nikon 16-85 VR.
Btw.: Is the kit-lens of your GF already stabilized (look out for the VR moniker)?
The lens that comes with the D60 and D5000 as standard in the kit is the 18-55 VR. But, as I say, she has problems with the pictures not coming out sharp enough and encounters noise/graininess at low lighting.
So, bearing this in mind, would these problems mainly be due to the settings she's using? Or would a new lens (even if MF was the only option) still be a far better route (obviously whilst using the best settings as well)?
I've been trying to read a little bit about camera settings. Am I right in thinking the ISO should be as low as is possible to preserve as much detail, where possible? And if so, should this be compensated for by increasing the aperture? Sorry for asking some basic photography 101 here, I'm just trying to work it all out in my head so I get the right thing for her.
I do think she'd get even more frustrated, for now, trying to do everything with manual focus so ideally I would like an AF lens for the D5000, if getting a lens in the first place is the right option.
Thanks for all the responses so far, I'd heard these forums were friendly and I haven't been proven wrong!