If you insist. Get ready to tl;dr.
png, the portable network graphics file format, is a lossless image format, meaning it does not change the colours of the pixels when it is saved. Among other features is full support for 24-bit colour, meaning nearly all colours can be displayed. There are 8 bits of transparency, meaning there are 256 possible shades of transparency, ranging from nearly invisible to almost opaque.
Due to its losslessness and excellent transparency support, png is the most suitable file format for simple digital illustrations. It is the most efficient at handling simple patterns and colours found in such drawings, and thanks to the transparency, png graphics are very flexible, and will blend in with the site it is displayed on. Thus, the file size will be small.
jpg, the joint photographic experts group, also known as jpeg, jpe, jfif, and multiple other obscure file suffixes, is a lossy image format. This means that pixels will not be the exact colour they're supposed to be. For example, if one puts a red fill bucket in MS Paint and saves it as jpg, most pixels will subtly change their colours and are no longer pure red. Like png, jpg supports 24-bit colour. However, it lacks the ability to display transparent areas.
These properties make photos suitable to be saved in jpg. Since photos contain profusely large amounts of different colours, ranging from light skin tone to dark skin tone, to soft shadows, to bright colours and whatnot, the lossyness of jpg is not noticeable, whereas in a simple illustration, "crusty" colours will be noticeable. Since jpg saves photos efficiently, photos saved in jpg will have small file sizes, but drawings will have inflated file sizes.
gif, the last of the trio, stands for graphics interchange format. Like png, gif is lossless, so it avoids the "crusty" edges jpg possesses. However, gif only supports 8 bits of colour, meaning unlike the many millions png can display, gif is limited to 256. Due to the limited palette, many colours will be changed. Another downside from png is the even more limited transparency, which is limited to 1 bit. This means a pixel in a gif must either be fully invisible or completely opaque. One upside, though, is its support for animation. Some websites are even dedicated to hosting gif animations. This can sometimes result in a mixed blessing, as an especially long animation will make the gif huge and laggy.
Technically, png was intended to be the successor to gif, but png's lack of animation meant gif was still well respected on the internet. Like png, gif was supposed to handle digital illustrations well, albeit with a limited palette. Its lack of colours may lead to massive loss of quality, and huge increase in file size.
Since Flash, especially on Newgrounds, has higher focus on simplistic, cartoony, hand-drawn graphics, and not realistic graphics like a Pixar movie, jpg is out of the question. png and gif's effective illustration saving make these two the best choices. Furthermore, png is then superior to gif, due to its high amount of colours compared to gif. The difficulty of making animated icons further proves gif to be an impractical file format.
In conclusion, png is the most suitable file format.
24 minutes of writing, words: 543, "Characters remaining: 4,961"
Flesch-Kincaid grade level: 8.7
Bibliography
Portable Network Graphics, Wikipedia
Joint Photographic Experts Group, Wikipedia
Graphics Interchange Format, Wikipedia
Experimentation and original research
though i could have taken you too seriously.