Hate to say it, but the 420EX is a terrible candidate to use off-camera in any radio or non-TTL scheme (like the Yongnuo YN-560 gear), because it has no Manual mode. You can only really control its power in TTL, and Yongnuo manual triggers (like the YN-560-TX and RF-60x triggers) do not communicate TTL.
If you use it with the YN-560-TX/RF-602/RF-603/RF-603II/RF-605 triggers, it will only fire at full power.
You also can't really use Yongnuo's TTL add-on triggers (the YN-622s) with their respective transmitters because the 420EX is too old to do camera menu communication (only the 430EX II/580EX II and later speedlights can do that), and that's the communication protocol the 622s use to do power control. You'd only have TTL control, and that wouldn't work for triggering the YN-560s.
There are reasons today we tell people to start with Godox TT600 speedlights and a Godox X system transmitter. Just me, but forget about using the 420EX, and get another YN-560IV.