Well, the minimig will output whatever the game resolution is, or being generated, which is why it runs on 20 year old monitors.
The minimig is Scandoubled, so the minimum needed for VGA monitors (if they scan down that far, is 31khz. unless you Jumper the option back to 15Khz and it will run on retro monitors.
now the second, if you use 16:9, the minimig does not know what is being used to display, you will have stretching in the signal being displayed, minimig just sends out the signal. it is entirely up to your display device on how it displays its picture.
I have a Wide Screen TV, and it can be set forced in to 16:9 or 4:3. If I feed the tv A 4:3 signal when it is set to 16:9 then yes you will have stretching. If i force 4:3, then I get black borders on left or right. That is not minimig's fault, it is the TV's and how it handles screen mode's.
Most Widescreen TV's have on screen menu options to FORCE Screen mode's, so you tell it to FORCE 4:3, and you will get the left/right Black Border's. Unless the TV is intelligent enough and automatically select the TV type for you. (Not usually). Same goes for Widescreen monitors, they should have display options somewhere.
Before you buy, MAKE SURE the monitor has 31khz support. A lot of newer models do not.