Yes the bed in your picture does look like construction lumber to me, that's what reminded me of the woodgears plans. I definitely agree with you, using cheap wood for beginner projects is the way to go and can yield great results; the key is to put a little extra effort into the details to clean things up.
Matthias over at woodgears uses cheap lumber all the time, and makes awesome stuff with it. He has definitely inspired me to do the same. I bet you've already seen this, but if you look at
this page you will find more detailed instructions about three different size beds. There is no writeup for the bunk bed, but he based it on the same construction techniques used for the other beds.
I'll be interested to see what you come up with, I love seeing nice furniture made from 2Ă—4's.