My approach would be to look at pixel fonts
https://www.google.com.mx/search?q=pixel+fonts
The problem you will have is that on a pixel font, you can not control different sizes, you have for example a font of 10 px and that is it. You probably can not have it in another size.
But a cool workaround would be not to use Gimp, but to use a text editor. For example, Notepad++, and then configure your working font there. Settings > Style
I use a lot Verdana and it looks nice at 11px. Make some tests to see the size of the ascenders and descenders.
You can test any font on your system this way.
Another font that was designed for screen, before the sub-pixel era was Tahoma, and probably Calibri. Take a look at the Classical "Web safe" fonts.