Thanks for the response Coding Badly (I have to admit that your name made me smile!)
I aim to entertain.
By 'circuit' I meant the entire Arduino Duo board I've ordered (I now see I was not clear enough, sorry!)
I assume you meant "Due". The other boards will probably be easier to shrink for use in RC models.
Do I understand correctly that once I've developed the code on the Arduino Duo, I can transfer / copy it to an Atmel AVR and run it on that...
If you only use the Arduino functions and libraries, yes. (After you rebuild your sketch for an AVR based board.)
...adding any external circuitry necessary (e.g. LEDs, voltage regulators, inputs, etc.)?
The minimum number of external components necessary to get an AVR processor running is zero. A 10K pull-up resistor on RESET and a 0.1uF by-pass capacitor for each VCC / GND pair is very highly recommended which makes the typical minimum external component count 1 + 2*(number of VCC pins).
Do you know of any 'idiots guides' to this process, please, that you could direct me to?
The keyword is "standalone"...https://www.google.com/search?q=arduino+standalone
"attiny" will probably also be helpful...https://www.google.com/search?q=arduino+attiny