The rifles could share a 556 suppressor, but on the handgun it would be uncomfortable at best, and not cycle correctly at worse. I would up buying a 9mm suppressor so I could shoot it on my handguns and my 22LR rifles, and I intended to build a subsonic 300BLK AR (can also be used with my Guardian 9) but I ultimately bought a JR Carbine in 9mm to use with it.
The 223/556 will suppress 22lr, but the pistol may not cycle, and it will be very heavy on the pistol. A larger suppressor, such as a 9mm, will suppress the 22lr as well (not quite as well as a 22 suppressor, but still good) but MOST 9mm suppressors are not rated for 223/556, since it is a rifle round and has much higher pressures. Since you dont already have the 223/556, if you went with a 9mm rifle or a 300 BLK rifle, you could use your 9mm suppressor on it. The 300 BLK would likely have to be subsonic though, because full power loads would generate to much pressure.
Clear as mud? Generally a larger suppressor can shoot any smaller round, but handgun suppressors shouldnt be used on rifle rounds unless the manufacturer has rated it for that caliber.