Which type of crystal to use is related to your receiver only. The transmitter uses the same crystal for that specific frequency - no change there.
The single or double conversion difference depends on the circuitry within the receiver, and which type it needs. The receiver should say, right on top.
By the way, get a JR crystal for a JR receiver, Hitec crystal for a Hitec receiver, etcetera. Some of the crystals can be used in different receivers, but many of the guys at the LHS don't know, so just get the same brand and be done with the issue.