I just installed a Leviton PR180 motion detector in my shop area but I do not have magnetic rapid start ballasts so the lights flicker rather than coming on full when triggered from the motion detector.

Any recommendations on magnetic rapid start replacment ballasts? I have cheap 4' shop fixtures from Home Depot.

A relay will solve that.

Just any old type of 120v relay or something special?
I have three dual bulb lights in the circuit, I think they are all 40 watt bulbs.

I think relays and I picture Radio Shack relays with spade connectors. What would be sufficient for most electrical code?

A relay will solve that.

Hmm... first you have to determine the total load of your lights. There are lighting contactors made specifically for what you want to do. However, there are many general purpose relays / contactors which could work. Is your motion detector hard wired into the circuit? You'll need some place to put the relay, between the motion detector and the first light in the circuit. Again the relay / contactor sizing will be determined by the lighting load. And there is always Grainger.