Here's a chart showing all the various video and computer resolution "standards."
This writer has a Sharp Aquos LCD, suggests simply getting a TV that advertises compatibility with PC resolutions, and connecting using a DVI cable (since it's a digital signal). Note that full HD, or 1080p, contains 1920 x 1080 pixels. It also has some advancing tuning advice using PowerStrip software.
How to Connect Your TV to Your HDTV (Engadget)
Update: found this article, very good, argues that 720p is fine for most (vs. 1080p), with the exception of those choosing to use it for a computer monitor:
720p vs. 1080p HDTV: The final word (David Karney, CNet, December 2007)
HDTV Resolution Explained (David Katzmaier, CNet)