This totally depends on the kind of image you want to store.
PNG is a lossless compression format best suited for "vector-like" bitmap graphics (i.e. graphics with large, regular areas with the same colour and clearly defined edges; graphics containing clear text).
SVG is a vector format, best suited to contain vector graphics (in short, collections of geometrical elements instead of collections of pixels). SVG is limitlessly scalable, while bitmap graphics lose quality when enlarged.
JPG is a lossy compression format (among other things, it removes nuances in the image invisible to the human eye to save storage space). It is best suited for photographs; due to its compression method, it is not well suited for vector illustrations or text.
Browser compatibility:
PNG Graphics are supported across browsers, with the exception of IE 6 if the PNG contains alpha transparency (the transparent portions will be rendered as a solid grey), and all versions of IE if the PNG is inside a HTML element with opacity less than 100% (but that's an edge case).
SVG is not always an option yet because browser support is not 100% at the moment. There may also be other behavioural differences to a normal
<img>tag. Use this only if you know what you're doing.Standard JPG is supported across all browsers as long as saved in RGB mode rather than CMYK (if your program doesn't make the distinction, it probably is the default).