I don't really understand how the sizing works with tilesets to be honest though.
What size would one need for a 1920x1080 monitor for it to show correctly?
The minimum size of a Dwarf Fortress window is 80 tiles wide and 25 tiles tall. Most of the time, we only need to worry about the width, though.
80 • 24 = 1920
To use a tileset with 24-pixel-wide tiles, your screen needs to be at least 1920 pixels wide to display the minimum of 80 tiles. On a smaller screen, you would either not be able to see the full window or you'd have to scale down the size of the tiles for the window to fit.
I like to play 1x1 embarks, though, so I like to pick out tile sizes based on vertical resolution. To see an entire 1x1 embark at once, you need 50 vertical tiles (48 for the embark and 2 for the UI border).
1080 / 50 = 21.6
If I want to be able to see my entire embark on a 1920x1080 monitor, I need a tileset that's 21 pixels tall or smaller. I like to go for tilesets 20-pixels tall to leave room for the task bar and the game window's border for playing in windowed-mode.