I'd suggest buying one each of every DVD player model any local store carries. I could do that where I live and still have $1000 left.
Then set them all up side by side. Use the spare cash to get several copies of your favorite DVD, one for each player. Go to Radio Shack and get an audio/video switch that can handle the number of players you got. Connect each player's output to the switch, then connect the switch to your sound system and monitor. You may also want to get a multi-plug power strip. You'll need to plug all the players in at the same time.
Insert the DVD into each player. As best you can, start them all playing at the same time. Now use your Radio Shack switch to toggle beteen each player's output. Compare. Ask everyone in your family to compare. Get a consensus of which player looks and sounds the best and/or has the nicest/easiest control interface.
When you've found the best one from that lot, keep it. You wanted to spend $3000 so don't take the others back for a refund. Take them around your neighborhood and give one to any neighbor who doesn't already have a DVD player. You'll be a hit, trust me. AND you'll still have the best DVD player you could find for $3000!
