Quartz or Automatic Movement?

Here is my subjective take, I own and equally enjoy both.

Quartz 

Pros: Little to no servicing outside battery swaps (unless it's solar 😅). Inherently accurate, even a crappy one is 20sec/month. I love the science and mental imagery of quartz oscillation and tuning. Generally quartz is more robust to abuse and magnetism. Quartz is grab and go, no setting constantly. Easier to make a thinner watch, if that matters.

Cons: some people like the mechanical sweep, you only get a tick with quartz. Most analog quartz watches don't have precise enough stepper motors and geometric index application to hit every index dead on, which can look sloppy. High end quartz from Grand Seiko does it. Fewer compelling designs because mechanical is more popular. 

Mechanical/automatic 

Pros: that mesmerizing mechanical sweep at varying beat rates depending on the movement. Display case backs are amazing even on basic movements to me. Generally more compelling designs and selection given the popularity, subjectively. Incredibly interesting and complex movements like Omega's Coaxial.

Cons: less accurate, but not enough to matter for most purposes. They stop if you have a rotation and wear different watches, though this is actually a plus to some people, sometimes I enjoy setting a mechanical. More servicing, and with higher end mechanical movements the servicing is expensive and often only the manufacturer can do it. 

Not a complete list. In conclusion, I like and enjoy both and don't put one clearly above the other for every purpose, they both fit the hobby. 

If I would have to choose one, it will be automatic all the way. I personally like watches because of the mechanism of the movement - and to wind my watches every morning is like giving them life source to keep running.

A quartz movement is a spec of laboratory grown crystal attached to a silicon integrated electronic circuit, a battery and a motor.  All which can be machine produced for pennies without the involvement of a human.  It is incredible, accurate and inexpensive but it lacks soul.

An automatic is powered by the uncoiling of a main spring which powers an entire drive train, where a palate fork reverses the motion of a balance wheel and gears all have to be hobbed to have the correct amount of teeth and ratio to keep time by mechanical means and a rotor has to swing in order to coil the spring again.  An incredible amount of design, manufacturing and hand assembly goes into the automatic movement and that give the watch soul.

I choose automatic and salute all the watchmakers who have made time telling possible without electronics.

Appreciate your eloquent detailed response.

respectfully

I own and enjoy both, however I lean more towards quartz as I am around strong magnets at work.

I own mechanical, quartz and digital watches. For me, it's more about the design of the watch and the emotional attachment I have towards it. 

Sometimes I like watching the sweeping seconds hand and hearing the watch tick when placing it to me ear. Other times, I appreciate the practicality and accuracy of a watch I can pick-up off a counter or from watch box and not have to worry about winding it and setting the time and date.

Your best bang-for-the-buck will most likely be a quartz watch, given the costs of movements. But another option is a mecaquartz movement, giving you the lower maintenance of a quartz watch, but the hand movement of a mechanical watch.