The "K03" portion of the 3k/warner part number only refers to the basic frame/bearing size of the turbo, there are many variations within a given frame size. There are lots of different compressor/turbine wheels, trims and housings. By the sounds of it you got a turbo from a VW 1.8T gas engine. They are capable of moving a bunch more air but at lower pressure than the diesel version, best suited to high revving gas engines.
As for upgrades, There aren't really any that will bolt up to the K03 flange. Your best bet for easy bolt on (high rpm) power would be the K24 or T3 from a VW 1.6TD. You'll need the 1.6TD exhaust manifold and you'll need to do some work on the oil lines and downpipe. The manifold and turbo will bolt on after some "clearancing" work on the intake manifold. If you love low rpm torque and aren't going for maximum hp, the K14 from early 1.9TD's works well, same installation drill as the K24 or T3, you need the manifold and downpipe/oil line mods will be needed.