I've played my downloads on the tv two ways -
1) I have the cable that allows my ipod to be hooked up to the tv. I have both a component cable and a composite cable since our tv's have different requirements.
2) I have another cable that allows my laptop be hooked up to the tv. It is called an HDMI cable.
If you are going to get any cables, I would suggest you get them off the internet. The composite/component cables are $40+ in the stores and the HDMI cables are $20+. All can be purchase on ebay for a fraction of a cost. That is where I got mine and they work great.
Apple has a guide that shows you what type of cable goes with every ipod.
Hope this helps!