Sean,
Processing is important in new sets as they have over 2 million fixed pixels (1920x1080) and most of the content we watched is at lower resolutions. You need a good processor to convert the signal (essentially fast at math right?). The chips in the TVs are very inexpensive chips typically. More expensive chips are in the higher end sets,
Example from one manufacturer. . .Sony(may have changed slightly, but still relevant)
Their LCDs have Bravia Engine, Bravia Engine 2, Bravia Engine Pro, XBR. As you go up the ladder, you get better processing.
The processors in receivers are typically a step up from those in most TV sets. If you buy a receiver with a processor inside, you can go down a model or two in the TV as you no longer fully utilize its processor. The receiver gives it the right amount of pixels, and the TV processor doesn’t have to work as hard.
Buy a receiver with built in processing, and then buy a TV with high refresh rate 120 or 240 Hz, and high contrast ratio and viewing angle.
This should give you the best bang for your buck.