I use PNG for all screenshot images. jpeg imparts artifacts due to the lossy compression which tends to have issues with text and other details, and I just don't like it even if the text is still fairly readable. GIF uses an older compression scheme, so tends to be larger than just saving a 256-color PNG.
Here's a picture saved for all three. This is a Photoshop Window with the thing I was fiddling with at the time open- though it might actually be affecting the results in some way here.
GIF - 377K
Text is perfectly clear. The image contents itself are pretty good too considering- the palette likely leaned heavily towards blues.
PNG - 335K
Looks identical to the GIF file- but is smaller due to a better compression algorithm.
JPEG - 269K
I had to reduce this to the 50% quality in order to compete size-wise with the other two. The text is still readable, so it still does the job here, but it does contain JPEG artifacts around the text and other on-screen elements. I personally don't think it is worth the trade-off; Mind, thjis is also why I don't use MP3 for the most part, preferring FLAC instead, so probably a personal preference thing altogether.