As noise is a special issue for you I will address that point.

In general the larger the sensor, the less noise.

In terms of value for money that means you should look at used DSLRs or Compact System Cameras, anything from the last four or five years, using an APS-C sized sensor.

As a general technique you can minimize the effect of noise in a shot by taking an exposure on a tripod and allowing the exposure take as long as needed to use base ISO ( typically ISO 100 or 200, depending on the camera ).

If noise reduction concerns you, then shoot RAW and you should be able to "develop" the RAW in software with whatever amount of noise reduction you want, including none.

Stacking images with a modern large sensor camera shooting at low ISO probably isn't required, but in case even the extremely low level of noise in those shots bothers you, you can of course stack.

The lens geometry has to be identical for every shot of a given subject, in order for the software to make the assumptions it needs to make.

You should note that all lenses have some distortion, and eliminating this can be partly ( largely ) achieved during conversion from RAW to JPEG. Your processed shots with be consistent even after this processing.

The focal length choice is tricky as it depends on how wide an angle you want to shoot. The typical standard zoom on APS-C systems is an 18-55mm, which covers a good range for normal use. For your purposes you might consider other lenses, like a low distortion single focal length lens, but I would recommend that you get the so-called "kit" lens anyway, as you might use the camera for normal shooting anyway.

As you are very particular about optics I would avoid the compact system cameras, as they often rely more on software or firmware correction of optics than DSLR lenses. So a used DSLR would be the direction I'd suggest.