So would want to avoid spyware or rootkits, for example.
Things I can think of are:
Wipe the hard disk, re-install the OS (I have genuine key and installer).
That to me seems enough.
That should be enough.
What about on the BIOS? Anything I can do here?
It is technically possible to infect a BIOS, but this is not something I ever saw live. If you are almost paranoid you could download the newest version of the BIOS and flash that, but it really should not be nesessary.
Having written that, feel free to check which BIOS version is installed; to check which version is the latest in the manufacturers website and what the changes are. If there is a newer version and if those changes are relevant to you then updating the BIOS is a good idea. Just not for security reasons.
Any other precautions I should take.
Just the normal ones when buying a second hand computer:
- Check the hardware for damage.
- Make a list of all hardware (so you know which drivers need to be installed)
- Install a fresh OS from a known good source.
- Install drivers (most should be auto detected. For those which are not see the second bullet point to help you know what to download.
- Make a backup of the clean system. Useful if you ever need to restore.
One common precaution though: Do not reinstall and then run windows update on an network full of infected computers. You may get a worm/virus before the windows updates are downloaded and install. (Sadly this is experience gained by reinstalling windows 98 while I was on campus. lots of students with infected computers.)