Electronic – slow down a 3 speed motor

DC motors don't work well at low RPMs. They stall and have horrible torque. (i.e. they can't turn very hard) So people have created gear motors: motors with integrated gearing. The result looks like a slightly bulkier motor, but one that has low RPMs and high torque. If you were to take apart a running a gear motor, you'd see the motor part actually runs at several thousand RPMs, but it's geared down to something like 60 RPM max.

A common specialized one is the standard hobby servo, which has some additional electronic bits but is fundamentally a gear motor. Check out any place that sells motors for robotics or surplus electronics and you'll see several different gear motors to choose from.

DC gear motors are controlled just like normal DC motors, so an Arduino motor shield works just fine with them.

Voice of experience: Use a jackshaft and additional belts/pulleys, &/or change to a different motor (DC with DC speed controller or 3-phase + VFD (variable frequency drive) variable speed.) The DC motor and speed control can often be salvaged from a treadmill that someone gave up on using, for free.

The fundamental limitation of running induction motors slowly on household (60 cycle per second, 3600 cycles per minute) AC is that the motor type you have has 4 poles if it runs 1800 RPM - so you'd need 36 poles to turn 200 RPM on 60-cycle AC. That would be a very rare bird indeed. You're actually fortunate if your drill press motor is not 3600 RPM to start with...

The other limitations (which apply to "universal" motors that can more easily be speed controlled, but are terribly noisy by comparison)(and also to DC, and to a slightly smaller extent 3-phase + VFD) are terrible (worse than a linear reduction) torque, and poor cooling/overheating since the motor's (built-in) fans are not running at a reasonable speed to cool it.

You might find gearmotors (normal motor speed of 3600 or 1800 RPM and an attached reduction gear) that run that slowly, but you won't like the price, especially if you want much power/torque.

The initial cost of the drillpress you are starting from has little impact on the cost of doing non-standard things with it (and may make a more expensive model that has better features such as dual reduction or a wider reduction range already built in look less expensive in the end.) Then again, you may be starting with completely the wrong tool - metalworking lathes are not too hard to find used affordably in moderate sizes, and typically have a "back-gear" setup standard that offers very low speed and high torque. Good for coil-winding (at a guess since you don't say and this is EE.)