I remember using silicon rectifiers in projects in the mid to late 60s, by then they were well accepted components. I remember frying the copper oxide rectifier in my brother's model train PSU when I must have been 10 or 11 around 1960 and my dad replaced them with silicon ones then. It helped that he worked for the company that made them.
Older car battery chargers consist of a fuse, small 50hz step-down transformer (30W maybe), and a rectifier. My oldest charger has a single multi-finned copper oxide rectifier, so the output is DC half-wave pulses. The voltage is too high for electroplating, it's hopeless for electronics, and doesn't light 12v bulbs to full brilliance. Good for rough work only, like charging car batteries. Not ideal for that either, because the owner has to disconnect them before they damage batteries by overcharging them. A later model is much the same except it has a moving iron ammeter, and a silicon bridge rectifier. Much better because the ammeter indicates when the battery is charged, more-or-less!
Modern chargers tend to have a switched-mode power supply and electronics that adjust the charge to suit the battery. Not much good for anything else unless perchance the load looks like a battery, which it might. How clean the DC is depends on the unit – anything between spikes and a steady current.
As already said, computer power supplies are probably the best cheap source of clean DC power. However, I prefer cheap readily available LED power-supplies because they come with terminals in a neat rectangular steel box. (They're a nicht-gerfinger poken component, and need to inside a user provided enclosure.)
This type provide well regulated fairly clean DC, and – even though not ideal for the purpose – will power a stepper motor.
For electronic experimentation, it's better to invest in a purpose made bench power supply that provides the voltages needed, with clean metered well-regulated DC and over-current protection. Ideally one with a big 50Hz transformer for low noise, but the switch-mode type are usually satisfactory. Picture is just an example – I don't own one!
I snoop round Aldi/Lidl whenever I get the chance – picked up a few repurposing opportunities, and a pair of just-the-job steel toe-capped trainers.
Back to modern times !Starting with a suitable 12V battery charger ! if it has a large finned rectifier remove it noting wiring. A small block rectifier say 50V or higher and 25A bolted on to a bit of ali has 4 terminals- Lucar. 2 have a squigle line this is AC from the transformer the other 2 have a + and a – this is the DC ! A cap across the output will give some smoothing, for regulation a regulator of 12v.and suitable capacity. Noel.
He does not tell what he wants to power – whether only 6V or 12V, current-rating etc., how critical it is, etc.Modern electronics wants 12V or 5V, for example, and very straight volts to close limits, too.
The blurb on its box, "fully-automatic microprocessor control", is not really relevant, since it follows that with stating its purpose: charging vehicle batteries, and I would expect those qualities in any modern vehicle battery charger. I would not expect very smooth d.c., and the control circuit might be regulated to supply the charging voltage (about 13.5V for a conventional lead-acid 12V battery), with some current limiting.
It may be suitable for other purposes if it can be connected via suitable smoothing and V or A regulator as necessary, which demands more than just sticking any old capacitor across it; but it is much better to select a PSU that will suit the purpose.
Alternatively, if the application is always 12V or 6V d.c., run that off a battery of cyclic type, and use the charger to fill that up again afterwards.
A 5V circuit would need a voltage regulator after the battery, unless it is designed to accommodate above 5V.