John: I've seen posts and notes showing what looks like two ways to do that, a 10 uf cap or a big resistor for possibly different rev UNO's or different Arduino boards... or just two different ways?
Two different ways. The auto-reset happens when the DTR signal goes low. This grounds one end of a tiny capacitor. The other end is connected to the Reset pin. The current needed to charge the tiny capacitor causes the voltage on the Reset pin to drop low enough to initiate a reset.
A low-value resistor (roughly 100 Ohms) between +5V and Reset provides current fast enough that the tiny capacitor does not draw the voltage below the Reset threshold.
Likewise a small capacitor (1 microFarad or more) provides enough capacitance that the existing pull-up resistor can keep the combined capacitors charged above the Reset threshold.
Either one will work.