The difference between HD Ready and Full HD sets is in the number of pixels they can display or their resolution. An HD Ready set will have a minimum resolution to be able to display 720 horizontal lines of pixels (compared to the 576 lines on a standard PAL display). This is generally referred as 720p (the p standing for progressive). A Full HD set will have a minimum resolution to display 1080 horizontal lines of pixels. You will see this as 1080i and 1080p (the i standing for interlaced, the p again standing for progressive). An interlaced signal is one where, each frame, every other horizontal line of the image is changed to the next frame. With a progressive signal, every single horizontal line of the signal is changed each frame. As a result, a progressive signal is generally less prone to flicker and should seem smoother.
Blu-Ray is one of the few formats which runs at a full 1080p. Most HD television broadcasts are broadcast at 1080i. Most games on HD capable consoles are in 720p (though a few are in 1080p). These can also be "upscaled" to 1080p by the console. Standard DVD video is in PAL and is generally output at 576p (again, upscaling DVD players can upscale these anywhere up to 1080p). Finally, standard television broadcasts are interlaced and are in PAL format and are therefore broadcast at 576i.
Therefore, if you're watching standard TV or DVDs, an HD Ready set is probably best. If you're interested in future proofing though, with Blu-Ray and potentially gaming as well as HD broadcasts, a Full HD set would be better.