Lot's of good advice here. Let me throw in a a little more, as I've done a lot of MD recording of live music where quality was important.
First, there -are- a lot of issues with your built-in preamp. It is fairly noisy, overloads pretty easy, has limited frequency response, and doesn't match up to the quality of an external preamp. However, just adding an external preamp doesn't solve all your problems. You now have to deal with an extra box, power issues, cords, more level setting, etc.
Here are some hints to make the most of your unit as-is:
1) forget whatever noise you hear with nothing plugged in. Unterminated mic-preamps will pick up all sorts of electrical noise that goes away with a mic plugged in.
2) make sure you are setting the preamp gain to the lowest possible level to get a decent recording level. Since we desperately want to avoid digital clipping, you should be pretty conservative about the level setting anyway.
3) never, ever use the automatic gain (aka auto level) for mic recordings. It produces all sorts of artifacts (popping, "breathing", clipping, etc.).
4) get a better microphone. The Audio Technical A-T 822/824 are nice stereo condensor mics made especially for use with portable recorders and camcorders. They are self-powered, easy to position, fit a regular mic stand, and provide a good level signal to your MD unit.
5) forget noise reduction software or hardware. Reduce noise at the source, don't try to remove it later. All noise reduction methods are a compromise and are not suitable for most digital recording methods (unless you're recording in a physically noisy environment and need to remove that noise during editing).
Alternatively, you can get into the area of using an external mic preamp. Sound Professionals makes one just for use with portable devices. A more budget minded, but less portable, solution is M-Audio's Audio Buddy mic pre. It is about $99 retail, has two decent preamps, phantom power for professional condensor microphones, and a selectable output level (-10db or +4db, -10 being the choice for your MD unit or any consumer gear). Also, with that in hand, you can buy a pair of inexpensive condensor mics that will shame your little Sony microphone. Oktava's MC1202 is a great choice and are often on sale for under $120 a pair.
Hope this helps some, and good luck. Half the fun is trying to get the most out of what you have, so start with that.
:cool: