I would like to record meetings with a small, handheld digital recorder, but
the one I have (a Vox Recorder from Radio Shack) results in very poor
quality, even on the best settings. Basically, I want to be able to set the
recorder out on a conference table and get the best possible recording for a
reasonable price, say under $200.00. Most of the voices will be within 10 to
15 feet. I have even used Cool Edit 2 to remove the noise, and amplify the
sound, but this only goes so far, and seems to make the voices somewhat
distorted.

I even bought two different types of microphones, a mini and a "full" size,
but neither seemed to make a difference.

Any advise would be appreciated.

I would like to record meetings with a small, handheld digital recorder

Have you considered MiniDisc?