For fitting screens while maintaining an integer scaling value, what I did was set an upper and lower breakpoint for width and height, for each scaling value. Meaning, if the game window is under say 1080x640, you go 1x. Once both width and height are above that, pop into 2x. Same for 3x, all the way to 8x. It takes some testing, but once you get the values right, the game will look good and crisp on nearly every screen. The vast majority will have the entire screen filled, a minority will have some letterboxing. Look here for what resolutions are worth testing up front (you can expand the display resolution line item):
https://store.steampowered.com/hwsurvey/Steam-Hardware-Software-Survey-Welcome-t...