Hi Dale,
If you like the sound from your digital piano, then the best thing is to record that with Audacity.

To do this, simply take take a cable from the earphone output on your keyboard, and plug the other end into your soundcard and use Audacity to record the wave file, and create the MP3. (Alternatively you can record from a micophone with audacity)

If you are looking for a better piano sound, then the situation is different. This create a midi file, either through getting your keyboard doing it directly (if it has the facility) or plug a midi cable into the midi out on your keyboard, and the plug the other end into the midi in on your sound card (if it has one). Use Composer to record your actualy playing.

If you go for the midi approach, then you need some good piano sound system to convert midi instruction into an audio sound. As I indicated in an earlier answer, there are lots of solutions to this, all will cost you money. I like the piano on Roland VSC. Garritan GPO have grand piano's in their orchestral systems, and I would assume other pianos in the band and jazz packages.

Your last paragraph:
Since I'd like my music to sound like a real grand piano instead of the typical "midi piano sound" is there a product which will "override" the music effects on my sound card (or wherever they come from) and provide an authentic "Carnegie Hall" piano sound? And would it be compatible with Audacity?

seems to me to imply that you want to go the midi method, and then use another package to create the sound. You can do this easily , and also in Composer when you tell the system which device you want to use to create your sounds, then that will automatically switch of your sound card generated midi sound.

(Incidentally I do something similiar to all this every day, except instead of piano sounds I have organ sounds. I play it on my Roland Atelier organ, it generates a midi file, I use that in Composer to correct my errors in playing, I then play using Composer that corrected music through some better organ sounds (from www.crumhorn-labs.com) and then use Audacity to create my MP3 file, which I then upload to my web page - www.smallchurchmusic.com ).

Cheers ... Clyde