Well, do you have a file size or resolution in mind?
You most likely want PNG; better compression and more options than GIF, and loss-less so while the file might be bigger than a JPG there won't be any compression artifacts.
A lot more detail is possible, the source is a vector file with no upper limit on resolution. At some point there's no more information in higher resolutions but where that point is, is not obvious.
Well, there aren't all that many colors in there. Looks like seven bits is enough. So let's try it at the high resolution with 7-bit color instead of 24 bit.