Interesting interpretation. :-)  For your purposes, you might try
resizing in terms of pixels, since your goal is on-screen viewing.  That
will make them a more consistent size (e.g., Windows wallpaper is
commonly 1280x1024 or 1024x768).

<rambling>

Try this on for size (trying not to be too technical, but explain the
factors involved)...

Each pixel is a colored dot in the picture.  The physical size of the
image depends upon how the dots get used.

For example, photos squeeze 300 tiny pixels per inch, while a PC screen
uses about 72 larger pixels per inch.  So, the same number of pixels
will make a larger image on a PC screen than a print.  (But the
trade-off is that the individual dots are nearly imperceptible in the
print, which makes for a higher-quality image.)

So, pixels decide the height and width of an image.

Then there is "color depth", a range of numbers that describe the shade
of color for each pixel.  A wider range of numbers = more shades of
colors = more disk space required.  The game is to make the color depth
"rich enough" to look good, but not take too much disk space.

Lastly, there is compression, to make the files smaller.

File types like JPEG have built-in compression.  The game here is to
squeeze out enough information to make the file smaller, but not so much
that the image looks bad.  There are settings to control how aggressive
the compression is, with these trade-offs.

When you resize an image, it's very possible the tool is using higher
compression, and maybe also reducing the color depth.  This will make a
dramatically smaller file, but lose quality at the same time.

All that said, if you resize to the pixel dimensions above and select
"high quality" (e.g., little or no compression), you'll end up with
good-quality screen-sized images that you can use for PC wallpaper if
you like.

Cheers,
Richard