gif's tend to be a bit tacky and rubbishy due to the limited colours.
This is not always true. PS gives a great preview of the effect when you convert to indexed color. Even at the maximum gif palette, 256 colors, you can get very little image loss. I've seen jpg compressed images that look just horrid, with all sorts of compression artifacts in what are supposed to be smooth flat color areas . . . convert it to .gif and it smooths those out, and doesn't lose any of the vital tonal changes.
And, in many cases, a .gif of equal compression in .png can be much smaller. You really have to experiment with **all** possibilities, especially if the file is going to exceed 3 - 5 K.