I raised this issue when the default style sheets changed radically in Mathematica 9.
In that version, there was an option to keep the older default style sheet for old notebooks, and you could deliberately select the older style sheet for new documents.
You can edit the default stylesheet -- it's just a notebook, after all. It is tedious, but you can change the fonts to whatever you want. The problem is that this stylesheet will revert with each update. If you send a notebook to another person, they will see it with their default stylesheet.
The best solution I came up with, which I use when it matters to me, is to make a custom stylesheet with a better choice of fonts, and use this as the private stylesheet for the notebooks in question. If you just point to a private stylesheet, any notebooks you send or can't link to will have a missing stylesheet error.
If you go this route, DO NOT edit the styles for Input or Code. You will screw things up royally if you do so. There may be other similar styles that need this type of care.
The better solution would be for Wolfram Research to change their default stylesheets to something a bit more useful or aesthetically pleasing. I prefer my body text to be seriffed, and for my Sans Serif fonts to distinguish between "I", "l", and "1" -- note that whatever this website uses fails in this regard.
I also prefer slashed zeros, ligatures and other typographic niceties, but this is not a word processor, after all.
At one time, seriffed fonts did not look good on a CRT. Those days are gone. Even non-Retina displays can show pretty much any type face well.
I hope that someone from Wolfram Reserch will respond on this thread.