Built-in Optical Triggers
If you're shooting in studio conditions, you could use the S1/S2 optical slave modes built into both of your flashes and your pop-up flash (if you have one) as the master trigger. This will have a more limited range and require line-of-sight between the master and slaves, and be less reliable outside in bright sunshine without bounce surfaces around. But it should work. In S1 mode, your pop-up flash must be in M mode (no preflash), and in S2, your pop-up flash must be in eTTL with Canon's wireless function turned off (single pre-flash). Canon's optical wireless system is a different triggering system that uses multiple preflashes; S2 mode can only ignore a single preflash.
Adding Radio Triggers
If you need reliability outside in bright sunlight or need to ditch line-of-sight requirements, then radio triggers will work. But, of course, you won't have remote power control/TTL/HSS with your Insignia, if you get manual triggers, and if you get TTL triggers, you won't have remote control/TTL/HSS over the YN-560III. (For definitions of TTL, HSS, etc., see What features should one look for when selecting a flash?)
Your dilemma: Manual vs. TTL triggers
Yongnuo makes both manual and TTL triggers, but they do not interoperate with each other. You could get a YN-560-TX transmitter which can remote power/zoom/group control your YN-560III through its built-in receiver. Then you could add on an RF-605 to your Insignia flash, and be able to turn its group on/off and fire it remotely, but you won't have power or zoom control.
You could also get a YN-622-TX transmitter, and add YN-622C transceivers to both flashes. You'd have TTL, HSS (if the Insignia can perform this--it may not be able to), and remote power/zoom control over the Insignia, but you could only remotely fire the YN-560III (it only has one pin on its foot, and that's for the fire signal. All the other pins are needed for everything else).
If you can afford it, I'd actually recommend ditching both the Insignia and the Yongnuo, and consider Godox flashes, like the TT-600 (manual) and TT685 (TTL), which can both be power and HSS controlled from the Godox X1, as well as giving you TTL access to any flashes that have them. A TT-600 and X1 transmitter cost roughly the same amount as a YN-560IV/YN-660 and a YN-560-TX, and the system can let you grow your lights up to studio strobes, if you want. Yongnuo never designed their speedlights/triggers as an overall system, while Godox did.
Of course, this may all change, as the world of cheap Chinese speedlights revolves quickly. The flashhavoc blog is a good source of information on what's current.