If I want to add an outlet on a 20 amp circuit should I use a 20 amp outlet & #12 conductor?

Unless you are in Canada you do not need to use a 20A receptacle.
#12 would be correct.

While using a 20 Amp receptacle is not a requirement here in the U.S. yet, for purposes of identification, you should use the correct receptacle.

While you will always know that the circuit is 20 amp, anyone coming behind you will not. It's a small thing, but you did change this circuit.

Is this an independent circuit or did you just add it on to a previous circuit?

If you added it on to a previous circuit and that circuit was 15 amp, the entire circuit is 15 amp. If you changed the breaker to 20 amp, then you have a problem. All of the wiring in the circuit must be upgraded to 12AWG,

While using a 20 Amp receptacle is not a requirement here in the U.S. yet, for purposes of identification, you should use the correct receptacle.

While you will always know that the circuit is 20 amp, anyone coming behind you will not. Its a small thing, but you did change this circuit.Don, I am not sure why this matters.
Also, a 15A receptacle (in this and most cases like it) IS most certainly the "correct" receptacle.

If you want to do this to tell quickly which circuits are 20A that's fine too.