Thanks, Daniel. I should have been more specific with my questions.
I did start with a Google search, and though I found a couple of relevant posts, they were a little hard to follow for a person who doesn't have much experience with R/C. Sheepishly, I admit that I'm hoping someone will say "make sure you get a transmitter that does X, or be careful about Y, and so forth.
This posting was very detailed, but with its discussion of trainer modules, PPM frames, etc, it quickly went beyond my comprehension:
It stands to reason that an R/C receiver can generate pulses to control servos the way I have already done with the Arduino, but I was concerned about just plugging it in to one of the digital inputs and trying to read the value. Does anyone have words of caution before I just try that?