It's a minefield.
HD Ready is a recognised standard - but even then there are variations -
280x720 @ 50 and 60Hz progressive (720p), and
1920x1080 @ 50 and 60Hz interlaced (1080i)
Obviously 1080i is superior to 720i, and that is reflected in the price. However, several independent tests have shown that the majority of users in their home will not be able to tell the difference between the two.
HD compatible is a very grey area used by manufacturers and retailers to confuse. The resolution is no where near good enough to show true hd, but you will see a picture. As any tv will display the tv picture through a hd box, whether it is deemed hd compatible or not.
However, it should be 'better' than a non-hd compatible (or comparable) tv.
Unless you need to buy a tv today because you don't have one at all - I strongly suggest you wait at least 6 months before buying any HD tv. The prices are constantly falling and the 'market' is settling down, to bring out properly recognised standards.