Usually most of the problems you get with older equipment (particularly stuff that runs warm or hot) are caused by the deterioration of the electrolytic capacitors used in them. They have a rated lifetime at a specified temperature, the lower their operating temperature, the longer they last. Usage also affects their lifetime, as they need to remain in use to survive, leave them discharged for ages and they'll age faster. They are the sleeved aluminium cans, usually made by elna, rubycon or nichicon in japanese equipment of this vintage.
These were the ones that came out of my luxman (from around 1984) Most of them were still measuring OK, but a few of them were dead. Only one was totally gone, which is the slightly discoloured one on the left but the others that were unhealthy showed no signs of age as it's all internal.
There should be a few large filtration capacitors for the psu too. These will be quite expensive. It is not essential to replace them, but it would be wiser to avoid more problems in the future.
To replace the caps you need to choose replacements that match the originals. (in uF, the voltage rating needs to be the same or higher) Almost all electrolytic capacitors will be polarised meaning that one side is marked negative and the pcb should also be marked. (isn't always so pay attention to the polarisation before you remove the cap) Bipolar capacitors will not have this mark The capacitors get are:
Nichicon PW, PE, HE, ES, FG, KZ (ES is bipolar, but can be used in place of polar caps, good for signal path use where film is too large and there was a polar cap previously as they have much lower distortion vs polar)
Rubycon ZL, ZLG, ZLK, ZLJ, ZLH
Panasonic FM, FR, FC
The tools you'd need are a de-soldering pump, a soldering iron and some solder. If you can't solder yet, you can either give it a go and learn by practising on something sacrificial, or find someone who can service/repair the unit local to you. So far though, i've fixed 6 separate bits of hi-fi (one was a car radio) all with simple capacitor replacement. Ignoring the main filter caps, it usually costs about £20-30 in total to do everything. With the main filter caps this can increase by around £30-50 depending on the size/voltage rating and number of psu filters. (usually something like a pair of 10,000uF 50V caps. Those mundorf 15,000uF 63V caps in the image above set me back around £20 each, though i wouldn't bother with mundorfs next time as they cost more than they are worth, better to stick with BHC/Kemet or Evox Rifa.)
I would also advise you get some deoxit D5 and clean all of the switches and volume/tone controls. (not the buttons/knobs, but the variable resistor/switch parts inside the amp)
I enjoy quite bassy music so something with a decent bass output would probably be the best (but not too overwhelming)... and that's probably the only key feature I really want 
