Thanks to everyone who has replied to my original question. I now have some good ideas as to what phono preamp to look out for.
Your ideas, Jeff, about isolation are interesting -- however, I've never had a problem with sound being transfered through my stand to the stylus. You can punch the stand and not really hear anything. Not bad. But if you hit the turntable itself, well, any table will pick up noise at that point. I had heard of a few other DIY fix-its, including cutting racquetballs in half and place them under the rubber nubs under the platter. Since I've never needed to address that kind of a problem, I haven't tried that trick.
On the other hand, I do pick up directional electric noise. As the tone-arm angle shifts during play, an audible hum enters into the sound. I know it isn't a loose ground wire; it is the proximity to my TV set. I may eventually play with the placement of the equipment in my room maximizing the distance of the turntable away from the TV.