I decided to build a Colpitts oscillator after watching one of W2AEW's videos.
The only issue I ran into was that I had the power supply hooked up backwards, so when I initially connected it to the scope, the +12V shorted to ground (and it burned a small hookup wire in the process). I should have paid more attention to the testing that W2AEW describes in his video - on a second try, I was seeing -7V where I should have been seeing +5V. And I shouldn't have trusted the two hookup wires I was using to get from a computer power supply output to a circuit.
I also didn't have 2N2222 or 2N5904 transistors, I used 2N3904s, which seem to work fine.