I bought a 53" Sony rear projection tv (MPN: KP-53v75) in 1999.  At
that time, the salesman told me that the tv was "HDTV-ready" and that
all I would need when I wanted to upgrade to HD was a "set-top box." 
I've recently bought an xbox360, and want to buy a box that will allow
my tv to display input from the 360 in at least 720p.  I've tried
hooking it up directly to the tv through component cables, but it
won't display HD properly.  What exactly is this "set-top box" I need
to buy, and taking value into account, how much should I plan on
spending?

Have you connected your Xbox 360 correctly to your TV? There is a
switch to turn the HDTV signal 'on' on your 360's component cables. If
your TV has component connections you don't need a set top box to view
the 360 in high-definition.

To view over the air HD (which is free) you would need a set-top box
if your TV does not have a built-in tuner and an antenna to receive
the signals. The Zenith antenna is great for receiving HD signals:

http://www.amazon.com/Zenith-ZHDTV1-HDTV-UHF-Digital-Antenna/dp/B00006FXR9/sr=1-1/qid=1160940890/ref=sr_1_1/104-7202334-1922335?ie=UTF8&s=electronics

A set-top box is also called a "HDTV tuner". Samsung provides one for
$250 which you can use to receive free HDTV broadcasts. Just connect
the Zenith antenna to the tuner and connect the tuner to your TV
(using component or DVI connections, if your TV has them) and then you
are ready to enjoy HDTV.

http://www.crutchfield.com/S-6ilRDlXyGf7/cgi-bin/prodview.asp?i=305SIRT451