Right, when you connect your iPod to a stereo that has iPod functionality it will show the brand of the stereo (or make of car if it’s a factory system) on the screen and the iPod is controlled through the car stereo. On your JVC, when you plug your iPod in, find a “source” button on the stereo and push it to cycle through FM, AM, CD, etc. until you find iPod, and then go from there. If you select a song on your iPod and have it playing BEFORE plugging it in to your stereo it should start automatically playing that song, and continue in whatever playlist you picked the song from.
I have a JVC KD-R820BT and an 80-gig iPod Classic. Side note: once every so often (couple of times a month maybe) the JVC hangs up when selecting the iPod and it just flashes “loading” indefinitely. Turning the stereo off and on cures it.