Do you really need all in one?
Link and image (not submit) can both be handled with a hyperlink, "input" is a button or a sumit image.
They don't feel like a good fit for composition, but thats the first thing I would try.
You could build the control based on WebControl, override TagName and AddAttributesToRender.
http://msdn2.microsoft.com/en-us/library/k1x24e42(en-us,VS.80).aspx