In case you can’t read the text that gives the max size on avatars (since white on white is hard to read):
Maximum dimensions; width: 100 pixels, height: 100 pixels, file size: 9.95 KiB.
I’ve found that .jpg files can be memory hogs where as .gif and .png aren’t so bad. I’ll often crop what I want and then save it in all three file types to see which one fits the size restrictions the best. Here’s an article about the differences between gif jpg and png. And here’s one comparing gif vs jpg.