t/t motor external power supply

Those are all good suggestions, but do tell us what is the problem with the existing supply in that why do you need to improve on it.
Computer SMPS is big, and too powerful, old ones have degraded components, may not give good regulation.
A step down transformer, with a bridge rectifier, appropriate capacitor and 7812 regulator is good to 1 amp, provided the transformer is big enough.

So first tell us your problem.
 
If the pickup is of good quality, I would use a transformer based supply, as the load is constant more or less.
If your cartridge is so so or poor, the exercise becomes a waste of effort.

Then see if the motor spec shows how tolerant it is to voltage variation, and design the regulator if needed.
Otherwise a normal bridge with smoothing and pF capacitors is good enough.
SMPS could inject line noise, not really needed...wall warts for 2 amperes will be SMPS, a transformer would bee too big for a wall wart.
That is the basic supply according to me.
Now choose as per what is easily available to you in your part of the world.
 
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The problem in SMPS, especially in cheap unbranded wall warts, is poor design and cheap components, and also some components are left out, for example the small pF / nF capacitors that are used to filter high frequencies. So audio noise will be an issue.

So like I said, a DIY approach would be a transformer based unit.
12 V 2 A Meanwell would be around 900 here in India, about 9 Pounds of UK currency.
2 A lighting driver, about 2 pounds or less.
And DIY SMPS involves ferrite transformers, not quite everybody's cup of tea.