OK, here's a rundown on DF's display:
Firstly, and this is set in stone, the display is 80 characters across, and 25 characters tall. No matter what you set for your font and resolution, you will have an 80x25 display for characters. Setting your resolution bigger will just make the characters bigger.
Secondly, the fonts that ship with the game are:
curses_640x300 : Each character is 8x12
curses_800x600 : Each character is 10x12
Thirdly, when you specify a resolution, the font is resized as needed so that you have 80 characters across, and 25 tall.
OK, now let's examine the defaults listed in init.txt:
Setting the resolution to be 640x300, and using the 640x300 font, will result in the character width being (640 pixels / 80 characters) 8 pixels, and the height as (300 pixels / 25 characters) 12 pixels.
Setting the resolution to be 800x600, and using the 800x600 font, will result in the character width being (800 pixels / 80 characters) 10 pixels, and the height as (600 pixels / 25 characters) 24 pixels.
Wait a minute! Didn't I say the 800x600 font was only 12 pixels tall? I did, but this is before considering the stretching that occurs to make 25 character lines fill 600 pixels.
The upshot of all this can be summed up as:
1) You will always have an 80x25 display of characters. No setting will change this. You will always see exactly the same amount of text, map, and information in a 640x300 window as you would in a 1600x1200 window.
2) The resolution you specify will resize the font you have chosen so that 80 characters across and 25 tall fills the number of pixels you specified.
3) For a truly square aspect ratio, your window width should be 3.2 times your window height. However, neither font that the game comes with is defined as square.
Hope that helps.