Uh-oh, I sometimes take the easy way out (i.e., use whatever format is supported by the software I have in front of me)…

Text & Clipart — GIF or PNG format
Screenshots from Window — PNG format
Video & Photographs screenshots — JPG format

The article explains it more and also includes images comparing quality.

http://www.labnol.org/software/tutorials/best-file-format-for-screenshot-images/3917/