Ok, on to the one reservoir capacitor in the power supply circuit. This is C6 and its job is to provide a reserve of power in between peaks coming from the AC-to-DC conversion of the bridge rectifier 4 diodes.
Choosing a replacement cap for this power supply reservoir cap:
What voltage rating should I choose - In the original circuit, this is a 2200 uF cap rated for 63V. Looking at the schematic, the bridge is supposed to normally provide 53.5V. That's too high since ConradH advises us to keep the normal operating voltage of a cap at 60-70% of the cap's voltage rating. So, I don't want a 63V cap there; I want more like a 80V or 90V cap. Ok, so I'll be looking for a 80V or 100V voltage rating cap.
What kind (family or series) of cap is best here - This is a power supply cap, so the most-important characteristics are high ripple and low ESR. A higher ripple rating means the DC output by the cap will be smoother (and that means less noise) and the low ESR (effective resistance) means this cap will get less hot than a higher ESR cap (because higher resistance translates into higher temperature as the power bleeds off due to the resistance). So, I'll be looking for a capacitor family or series whose characteristics (from that family's datasheet) are high ripple and low ESR (as opposed to low leakage). The opinion I've heard most here on AK (thank you MarkTheFixer and others) is to choose the Nichicon PW series of caps for power supplies (or anything, really, that isn't carrying the actual audio signal). So, I looked for a cap in the PW series that was at least 2,200 uF "big" and could handle at least 80V, preferably 100V. There are none, at least none in that series that Mouser carries. So, the "how big a cap" will have to wait a little.
How big a cap should I choose for this - the 2200 uF is sufficient for the original design, its operating characteristics, and the components leading up to this cap. However, I'm OK with spending a little more money (usually less than a buck or two) to beef this component up. My ears aren't great, so my belief is that a slightly or somewhat larger cap here will provide additional power reserves for those unusual times when the music you're playing has great, sudden demands (dynamics) and you're playing it kinda loud (like more than 50% volume). Having another 20% or 50% reserve power should let this cap continue to feed the hungry power transistors, at least for a moment. There is lots of debate about this. I predict some of that debate will continue in this thread right after I hit "post". No matter. This is my opinion and I'm just sharing what logic and desire I used to choose this particular cap. So, if 2200 uF is what the circuit called for initially, I'll be looking for the next couple of sizes larger than that: 3300 uF and maybe even 4700 uF (typical increments in many cap families).
Searching on Mouser for Nichicon, through hole mount, over 2200 uF, 80V and 100V doesn't return many hits. That's because most of the caps in this capacitance range are so large they aren't commonly soldered to the PCB (i.e. through hole), so I remove the "through hole" parameter and let "snap in" and "screw terminal" mounting styles be included in the listing. NOW I'm getting plenty of hits. So, I sort the results by ripple, then diameter, then cost to get a feel for "what is available that will work", "what is available that is same-diameter or smaller (so it'll fit in the mounting collar)", and what are the lowest-cost few choices within those results.
What comes out of all this sorting and resorting is a 4700 uF 80V cap that is the same diameter as the original ELNA 2200/63 and isn't very expensive. It happens to be a snap-in and I can work with that.
The new, snap-in mounting style cap just needs some extra leg added to each terminal to give the original wires enough room to be attached.
The replacement fits in well and it looks good (even though no one will ever see this).
There is a big deal about bigger caps, though, and that is inrush current. As soon as you turn power on, the reservoir cap will want to fill up, the AC transformer will let in as much AC from the wall outlet as it can, and the components between the wall outlet and the reservoir cap will need to be strong enough to handle this short-lived peak flow of current. In this upgrade, I have upgraded the diodes to UF5404's and they can handle 3A continuous and something ridiculous peak. So, they will be OK. I knew I was jumping up (100% increase in capacitance), so I was careful when first turning on the unit and I've watched it carefully through dozens of hours of testing. So, in this particular case, a 100% increase in this cap's capacitance worked fine.
So, when I'm looking for a replacement cap for the reservoir cap (the first cap after the bridge rectifier), I'm looking for a big capacitance, higher voltage, similar diameter, high ripple, low ESR cap. And I don't care much about leakage. So, I'd be looking for something in the Nichicon PW series and, if I can't find what I need there, use the above parameters to search more broadly for something that has all the qualities I want from this specific-purpose position in the circuit.
There are often more than one secondary on the transformer. For instance there might be another lower-voltage secondary to power the tuner circuits and there is very often a much lower voltage secondary used to run the lamps. Those additional power supply circuits, if they rectify the AC, will likely have a reservoir cap, too. The same guidelines can above can be applied to those circuits. It might not be as useful since these circuits aren't supplying transistors that often deal with highly-varying demands (i.e. dynamic music), but the prices for these caps is gonna be really low due to their size and voltage, so what the heck. Go crazy.