I am looking for the best combination of picture quality and processing/movement speed for the money mentioned. I want a clear picture, no blur, no pixelization when the action is fast.

So can someone please list the best 50-75 inch rear projection hdtv's for under 4k, and the best 45-70inch plasma tv's for under 4k.

Please let me know asap.
Also, if you know a dependable site that will tell me this information, please give the link. thank you.

You'd better ask about this in the various display-related forums:

http://www.avsforum.com/avs-vb/forumdisplay.php?f=9

This forum is about OTA HD tuners, cable and satellite HD set-top boxes, antennas, etc.

if you are willing to spend up to 4k look at the pioneer 5020. You could possible also find the elite version of the set for under 4k too. This is almost always considered the best plasma tv on the market...

I'd recommend the Pioneer PRO-111FD KURO Elite. I just bought one off of Roman for less than you're asking.

As for rear projection televisions, they're either cheap (Samsung DLP with LED backlight - <$2000), mid-priced (Mitsubishi Diamond DLP - ~$3000) or really expensive (upcoming Mitsubishi LaserVue - $7000).

Again, wrong forum.