I have just bought an HD ready tv. Do I need to get an HD dvd player to...

...get the best image when I watch dvds? I only want to watch dvds, not record or have any special features, so I was going to get a cheap, basic dvd player but do I need to get an 'HD ready' dvd player to get the best picture??

Yeah. Blu-Ray player would be your best option.

it really depends on what you want to do.
there are two types of disc players now.
DVD players, which can only play DVD's
BLU RAY players, which can play blu ray and dvd's
now is the tough decision, do you want to get the player that will take full advantage of the investment you just made?
if you are not worried about it at all, go with a dvd player that can upconvert to 1080p, and has a HDMI output. These players can be found for less than 100$ and dvd's do cost less than blu ray movies.
the only thing to remember, the sound and picture quality will be a little be less than that of a blu ray movie.
The movie from the dvd is still at best 480p in resolution, the player just upconverts the signal and interpolates the extra info needed to create the 1080p signal.
i have a 1080p tv with a blu ray and some movies i still buy on dvd, just because if its a drama or something that doesnt have alot of imagery or action with great sound, why pay more for the movie. but some movies, like the fifth element, dark knight, sunshine, etc..., i can really tell the difference watching and hearing it on blu ray. but again the movie can cost a little more sometimes.

Get a DVD player that outputs 1080p (HD) to get the best picture. You can also buy an upconverting 1080i dvd player, but you will not see nearly the same resolution from it.

There are several products that output in 1080. They are PS3's, Xbox360's, Blue-ray players, HD-DVD players, etc. Of those, the HD-DVD's are being phased out.

Now would be a good time to look into a PS3. You get the game system and the blue-ray player all in one. ;)