You really should have gone for a basic EE course where they would have covered V=IR and P=IV and so on. That would really help your understanding of the basic circuit design. Calculus also helps, because you're talking about RC circuit design (http://othello.mech.northwestern.edu/ea3/book/elec5/RC.htm) and power supply design. In addition, you are throwing in semiconductor physics with the introduction of FETs.
Where your stray voltages are coming from: If you have -20 to +20 VAC coming out of your transformer (40V peak to peak), when you rectify it, you have approximately 0 to 18.6 V coming out of the rectifier (you lose 1.4V due to the silicon diodes in the rectifier, less if using germanium diodes). See http://content.answers.com/main/content/wp/en/6/6f/AC%2C_half-wave_and_full_wave_rectified_signals.PNG. Adding in the RC circuit will likely provide you with approximately 17.6 to 18.6 V (this is called 18.1VDC with a 1V peak to peak ripple). Not very clean. The tighter you design the RC circuit, the tighter the tolerances on your ripple voltage. There's a good power supply primer here: http://my.integritynet.com.au/purdic/power1.html
As to your question regarding the "shocking feeling" when touching the backside of your LM317...yes, you're now creating a new path to ground for the electrons in your circuit. Pin #2 on a TO-220 transistor package is hooked directly to the metal "back" of the case. That's why to add a heatsink to the TO-220 you need a mica insulator.
There's a reason we measure things with a multimeter and/or a laser thermometer. Touching things when you have electrons flowing is a very bad idea.
Also, you can do some reading here: http://www.allaboutcircuits.com
Where your stray voltages are coming from: If you have -20 to +20 VAC coming out of your transformer (40V peak to peak), when you rectify it, you have approximately 0 to 18.6 V coming out of the rectifier (you lose 1.4V due to the silicon diodes in the rectifier, less if using germanium diodes). See http://content.answers.com/main/content/wp/en/6/6f/AC%2C_half-wave_and_full_wave_rectified_signals.PNG. Adding in the RC circuit will likely provide you with approximately 17.6 to 18.6 V (this is called 18.1VDC with a 1V peak to peak ripple). Not very clean. The tighter you design the RC circuit, the tighter the tolerances on your ripple voltage. There's a good power supply primer here: http://my.integritynet.com.au/purdic/power1.html
As to your question regarding the "shocking feeling" when touching the backside of your LM317...yes, you're now creating a new path to ground for the electrons in your circuit. Pin #2 on a TO-220 transistor package is hooked directly to the metal "back" of the case. That's why to add a heatsink to the TO-220 you need a mica insulator.
There's a reason we measure things with a multimeter and/or a laser thermometer. Touching things when you have electrons flowing is a very bad idea.
Also, you can do some reading here: http://www.allaboutcircuits.com