Minefield.
“HD Ready” is a certification programme. “Full HD” isn’t. The correct term for “full HD” is “HD Ready 1080p” and this is usually what Full HD means, but there’s no guarantees. If you want a “full HD” set, read the tech specs carefully or you may get stiffed.
A “HD Ready” certified set must be able to display 720p and 1080i signals. “HD Ready 1080p,” as the name suggests, must additionally be able to display a 1080p image.
As for whether you need “full HD” (1080p) or not, it depends what you’re watching. Blu-ray can provide a 1080p source, as can some PCs. The PS3 and Xbox 360 can both provide a 1080p signal but whether they do or not depends on what you’re playing – ie, it’s up to the game developers what they put out. From experience, most don’t bother, presumably for performance reasons.
1080p is the best home reproduction you can get for all practical purposes. 1080i and 720p are inferior to 1080p but comparable to each other. Whether you would notice any real difference depends on a number of factors; size of set, viewing distance, how good your eyes are and how much you care, to name a few.