HDMI is a digital connection, it does not bestow 1080i or 1080P on anything it is connected to.
If you are looking for a new DVD player then you have the choice of a regular player with upscaling capabilities that will simulate a HD picture from your DVD's ant then pass it through the HDMI cable to your tv.
A HD DVD or Blu Ray player will output a true HD picture so no video trickery is used to provide a better picture. This of course gives the best picture, but will require that you purchase HD/Blu Ray discs for this, On a side note, most of these players will automatically upscale ordinary DVD's as well if that is all you have available.
Upscaling is not HD, it tries to provide a better picture but there is only so much you can do with the resolution on a regular DVD.
On a side note, your tv is already upscaling your video for you, the hope is that the player will do a better job.
I shall briefly cover the myth that is 1080i/1080p. If your TV can display a (p)rogressive picture 0f 1920x1080. A 1080(i)nterlaced picture displays with the same resolution, however it leaves your tv to de-interlace the picture and not all tv's do this very well. For all intents and purposes, most people wont even notice a difference.
If your tv is only able to display up to 720p natively, then don't bother getting anything outputting 1080i/p as your tv will automatically downscale the picture to fit its reduced resolution. The picture may appear sharper with this source, but only because there was more information there to begin with. It is a false economy until the prices drop dramaticaly.
Anyway, if it was me I would stick to a cheapish upscaling DVD player at the moment and when prices drop you can look at a true HD source. At that point, hopfully the war between HD DVD and Blu Ray may be over so you can choose your equipment with confidence.