Question: It seems to me that most caps on these systems are ripe for replacement. How should an amateur go about this? Shall I try to replace all caps that measure out of spec or only take one step at the time (for me it would probably be replace the caps on the power circuit board, then later move on to the caps Mika mentioned on the radio board).
Do the mandatory caps first - these are the small electrolytics in the power supply and the CPU board (maybe the front panel as well). No need to even measure them.
The rest is optional... the tuner problem is probably something else than caps, and it is easy to get back to that later anyway because the board is the first to come off.
Question: How do you guys repair a lifted trace? Are there any pens that can carry this sort of current or how do you save your boards once a trace has lifted? What is the best temperature to desolder caps with to avoid lifting traces perhaps 400 celcius?
The old soldering alloys that contain lead (and these were definitely used at the factory at that time) melt at about 180°C. Current lead-free solders melt/cure at about 220°C. The right temperature depends on your soldering iron. If it is slow to react to the cooling of the tip of the tip (so to speak) or the tip has poor heat transfer to the object, you may need a bit more to compensate. But 400°C is probably the upper limit, you shouldn't need that much - with a too hot iron, the resin evaporates off the solder making soldering difficult, and you will overheat the components and the PCB.
But don't use too low temp either, because then you will also overheat the components because (de)soldering takes so long. The "usual" tip temperature for lead-free solders is 350°C.
To help save the traces, don't start wiggling the components until the solder has actually melted through. With two-legged upright components such as most caps in this case, try to avoid pushing the opposite leg in while trying to pull the other out through the PCB. If the component is to be replaced anyway, you can cut the legs off first if there's space, and then easily remove them one by one.
And when the accident happens, I usually solder in a jumper wire if the next solder spot is very close (1 cm or so). For longer distances, it may be more sensible to scratch off the insulation on the trace and solder a short wire on top of that.