So what exactly would be the best power pack? Eventually, I will have 20 LED lights at 3v each so I need the right power.I would also advise against trying to rely on any old variable power supply to provide a specific voltage. For that matter, I'd be surprised if you can get that Tyco power pack to even put out a reliable 3 volts. These old things work on a variable resistor, which means even if you superglue the throttle in place, that voltage is going to drift from changes in temperature, humidity, or how many people are currently looking at it. In other words, there is no way to accurately lock it down to a specific voltage. And keep in mind that LEDs are very sensitive to voltage, so if you drift more than 1/4 to 1/2 of a volt, you're going to blow the LED.
The way I look at it, you could spend a couple bucks now for a small power pack that provides the correct fixed voltage, or you could replace your entire string of lamp posts every few months.