The definition of high-resolution of course depends to some extent on the end-purpose. If the image will be 5x5 cm in an article, the resolution in a screenshot or the exported PNGs should be enough, but if it goes on a poster and the image ends up being 20x20 cm, one may be stretching it somewhat.
Note that if you use Windows you do not need GIMP to make a screenshot, you can just use the "Snipping Tool". Or press Alt+PrintScreen to capture the current window, and paste it into Paint and save it as a PNG from there. Do not use JPG for screenshots, that format is not suitable.
Most LaTeX styles and publishing houses can use PNG directly these days, I think, so if there is quality loss due to the conversion from PNG to EPS, just stick to the PNG all the way.