To connect your iPhone, iPad or iPod to your home stereo you just need a 3.5mm to RCA cable like this cable above. The RCA cable plugs into the rear of your stereo and the 3.5mm plugs into your iPhone headphone jack.
When plugging into the back of the Stereo Amplifier, you can use almost whatever inout you want: CD-INPUT, TAPE-IN, TV-IN, DVD-IN or the AUX-IN, but do not use the PHONO-IN as it is designed specifically for a record player and won’t sound as good.
For the best results set your iPhone volume to about half. If it’s too quiet you may get noise and hiss. If it’s too loud you may get some distortion.
You can have the USB charger plugged into the iPod at the same time.
If you want you can use an Apple iPod dock, and leave the audio and charger cable plugged into the dock permanently. The dock has a line out so that it doesn’t matter what volume the iPod is set to, and it will also charge your iPod, and has a remote control.
As for what cable to buy, they start as cheaply as 1c (e.g. here) but I’d steer away from one like that which uses cheap cable. Pretty much anyone can tell the difference in the sound on one of these cheap cables even if you don’t know much about music at all. I use one like this which costs about $25, you can buy one somewhere in the middle for around $10 like this or this.
If you are buying a new Stereo, Pioneer and others are now including AIRPLAY into some of their amplifiers. The amplifiers have a Wi-Fi receiver built in which means you can play from your iOS device over your Wi-Fi (Airport) network directly to your Stereo with no loss of quality. You don’t need to connect any cables.