If PSU was tested prior acquiring and is known to be working, and you wish to use it daily, do the following:
1. Test the high voltage capacitors on the primary side for impedance and capacitance. Make sure they are symmetrical in specs, ideally, they shouldn't deviate more than 3% from one another. If they check out, don't replace them.
2. Test timing capacitors (usually 1-10uf electrolytic) next to the switching transistors on HV side, make sure that they are in spec and symmetrical. They are the main reason why HV side fails on old PSUs, once they dry out, switching transistors can't fully turn on and eventually overheat. I replace them without much thinking only with good brand capacitors.
3. Check output capacitors, if one of the same kind is OK, usually rest will be fine too, if not, replace them all.
4. Check underside for cold solder joints.
5. If a PSU doesn't have load resistors on all output rails, apply some load before powering it, or PSU will fail shortly. An old hard drive or some sacrificial motherboard usually are enough. Apply load even if it has load resistors, because w/o sufficient load, PSU won't reach right output voltages and might appear faulty.
If PSU wasn't tested prior acquisition and is in unknown state... Then test HV caps and if they are in spec, connect PSU to a variable voltage transformer and reform capacitors for at least two hours by increasing voltage in steps prior even attempting to power it on, else those caps might just short out almost instantly.
I wouldn't bother replacing the fan, if it's noisy, just clean and re-oil it. To be honest, it would be difficult to find a replacement for such a good quality fan.