I would just use a modern PSU.

I picked up a couple Seasonic Focus GX-850 PSUs earlier this year from Amazon specifically for that reason. I currently use one in my P4 system.

Agree

if your motherboard is ATX the best is get a recent good quality power supply
some modern ATX power supplies still have the split molex connector for ATX 1.0 and 2.0 no ? or if not I'm sure any aliexpress adapter will work

P3 and P4 do not rely on a strong 5v rail as much as the Athlon socket A does: the P3 only draws 6A max and the P4 relies on the 12v rail.

So for a good P3 system you need about 15A on the 5v rail. The 12v rail wil not have very much load.

For the P4 you need about 6A to 8A on the 12V rail depending on the psy, so any 12A capable psu wil do.
With these requirements about any modern half decent psu wil do.

You can get cheap adapter cables to acquire the needed (mini)molex connectors.

This will be far more reliable than any old psu that has not been recapped.

When I run out of psu's I'd definitely go this route too. Only the socket A Athlon wil be a challenge, as these easily require over 25A on the 5v rail.

For Socket A (and maybe even P4) I would look into NOS Enermax units. These are fairly good units for Athlon based systems - beware as you will have to pry them open and remove every trace of RTV glue though, due to it getting conductive from aging.

Another option would be Antec. These are easier to find I guess, being more popular at the time. As for the maintenance required on Antecs -probably bad caps if they are CWT or Seasonic built - Delta based Antecs usually have an D suffix in their model number and almost never require recap. (Delta knows their caps well enough)