You can buy the CD steppers with leadscrew on ebay very cheaply - eg
https://www.ebay.co.uk/itm/392331862778 (you will find cheaper ones than that). There are others with finer leadscrews if you need slower movement. Search for 'linear stepper'.
Steppers do need dual h-bridge drivers to operate them. If you use proper stepper drivers you will get all sorts of advantages but for a low-voltage stepper like the ones above you can still do them pretty cheaply with something like
https://www.ebay.co.uk/itm/173044559728I can't suggest any _cheap_ quiet servos - I'm afraid the only quiet servos I've seen are expensive ! But there may be other mechanisms like the CD sliders. For more powerful units, headlight positioners are worth considering. They're also stepper motors with a leadscrew. Mirror motors are more often just a geared DC motor and a cam.
If you have large numbers then pneumatics might be an answer : valves can be
https://www.ebay.co.uk/itm/254229792066 rather than something expensive from Festo. Actuators might be syringes, or small balloons. Pump might be a fish tank aeration pump. The thing about pneumatics is that you'll typically have one pump and lots of actuators rather than lots of motors, so it doesn't get noisier - unless you need a bigger pump, or let the air out too noisily.
Muscle wire has quite a small extension with heat, so if used in extension mode needs to be wrapped around pulleys to get enough length. If used in a bending mode they will give more movement, but then you need thicker wire.
You might learn something from
http://www.osloom.org/. I haven't seen updates for ages and I guess has been abandoned but they used muscle wire to avoid patents on many other forms of heddle actuator. It looks as though it had an acceptable level of performance but I don't know what happened to it.
Most of these aren't very accurate without feedback. But they're OK for pushing from one limit to another.