I have an Apple TV so I've been through the setup using an A/V receiver. If you wish to keep the TV you have, you need an A/V receiver instead of regular DVD player.
Apple TV2 outputs HDMI and the device it connects to will need HDMI inputs. I have a one year old Panasonic BluRay player plus a Sony progressive scan DVD player and neither supports HDMI inputs. If you can find a DVD player with an HDMI input, it is probably a combination A/V receiver and DVD player.
If connecting the Apple TV2 is your goal, look to an A/V receiver. You may find a receiver that also plays DVDs if you also want to play DVDs.
Apple TV2 now supports 720P which is better video than the RCA jacks can support. The good news is your TV supports component video which is a better way than using the RCA port for video. To use the component ports, you'll need component cables which are a step up from the RCA composite cables. For audio, you will need to use the composite RCA audio ports but at least you'll be watching an HD quality picture.