there isn't much point in connecting an hd converter the toshiba cx32g60. the tv can only support an sd signal (composite video or ntsc analog). however, many hd set-top boxes (dvd players, cable and satellite) have composite outputs. these can be connected to your tv. blu-ray videos can't be watched with this tv. (the hdcp (high definition copy protection) can't be sent through most converters.)
if you want to watch ota programming , the cheapest option would be to find an sd digital-to-analog converter. these were the ones sold when most stations switched to digital tuners. some are being sold off as people replace their old analog sets. there are some hd tuner boxes, like this one: http://www.solidsignal.com/pview.asp?mc=03&p=3500stb&d=iview-hd-dvr-receiverconverter-box-for-tv-antenna-qam-%283500stb%29&c=digital%20converter%20boxes&sku=
, that have composite video output which will connect to the cx32g60.
i hope this helps.
(if you tried an hdmi to component video converter followed by a component to composite video converter, the signal may degrade excessively.)