New_Noob,
You'll probably want to use the 12V power adapter. If wired in parallel, the voltage is constant across each LED. That is, 12V for each LED. The variable then is the amperage. Normally, you'll want to match the amperage of the LEDs to what's printed on the power source. Since we're talking about LEDs here, it doesn't make that much of a difference if they're overpowered a bit. They'll still last for many years unless a resistor burns out (which I have heard of happening with LEDs from autolumination).
The reason why some power supplies are more expensive than others is that some are regulated and others are not. That means, if you put a small LED by itself on a power supply, the voltage will still be 12V when the amperage isn't what the pack is supposed to put out (i.e. 300mA on a 300mA power supply). If you have an unregulated power supply and you don't match the amperage/resistance, then you're essentially overdriving the LEDs. The nice thing about LEDs is that they dont produce much heat at all, so they'll last long anyway. We're still talking about years of nice lighting.
oh yeah, don't connect a single LED to a power supply like I described unless you have the proper resistors. You'll cause a short. Just get it close.