How can I best amplify a signal from my headphone jack to operate a relay 3-32VDC?
Sometimes, simply stating what you're trying to accomplish is better than asking the question you think you want to ask.  This could very well be the case here.  So, indulge me as I try to restate your situation and provide some sort of answer.

You have a headphone jack with some music on it, and you want that music to control some lights.  You probably want the lights to blink or pulse with the music.  Right?

This type of device is called a Light Organ.  There are many forms of light organs, but I assure you that none of them use an op-amp driving a relay.  There are several reasons for this:  


Relays don't operate well from an audio signal.  They really want a signal that stays on or off for a while and doesn't just oscillate like an audio signal does.  
Relays can't dim a light.  They can turn one on or off.  Not so good at dimming.
Relays would make a lot of noise, chattering away with the music.  Not a pleasant sound.


I would recommend that you Google for "Light Organ".  When I did, I came up with 65 million pages.  Some of them are selling completed units, some have kits, and some have schematics.  

I hope that helps!