Our Map Tiles API and our Static Maps API both support a variety of image formats. We recommend using .png for most use-cases, but you can choose other formats for special situations.
The file size of an image is generally smaller with few colours (PNG files) and lower quality (JPG files), but the visual artefacts become fairly obvious. In particular, the particular colours used for each map image is calculated per-tile, after anti-aliasing, so it can be common for different tiles to have different available colours. Small colour palettes are best reserved for map styles that have only a few colours to begin with.