Most likely you cannot convert library ebook because they are DRM-infect. Unless you know how to disinfect them.
Assuming you don't know how to disinfect ebooks, mobi is not an option, it leaves you pdf and epub. PDF is an abomination for 6" screen, even though Sony Reader supports reflow. So, it leaves epub only
P.S. Probably all three formats are DRM infected, but Sony Reader doesn't support *.mobi