can I buy low resolution, black-and-white, text-only LCD monitor to save money and power?

The newer coke machines I have seen lately have displays with an array of pixels.

Deffinately look at that. The OLPC XO-1 was built to be cheap and run off very little power. The screen is/was estimated to cost $35 and the whole computer to consume only 2W and, at one point, was designed to be charged with a crank. Other than it not being a two line text screen, it seems to fit the profile of a low cost, low power computer/monitor solution.

Buy second hand, and focus on how to hook up such an used screen to your computer.

They’re nice for RPM readouts, or angles from a Hall effect encoder.
Sometimes you neither need nor want a full screen of pixels on the front of your circuit box.

What about the screens made for ATMs? or chartplotters or the larger dashboard GPS devices?

Speaking as someone who has to write UIs that run on a 4 line x 20 character display, I can tell you that they are a big pain. Graphical UIs are much easier and less restrictive than having to confine everything to 80 characters. We only use character displays in our product because they are cheap and require a puny processor to run them. If I had the horsepower, I would switch to a color LCD in a millisecond.

As for the OP, it’s pretty unclear what he wants. For specific applications (mostly embedded or annunciators), a one-or-two line character display is fine. For general computing (e.g. - surfing the web) they’re useless.