If your AR is a .223, then it will most likely have 1/2"x28 threads unless it is an HK 93 or some other Euro-trash gun

. Your threaded barrels for .22LR's are also likely going to be 1/2"x28. Technically you could use the same suppressor for all three, but a suppressor that will handle .223 is going to be fairly heavy on a pistol unless you go titanium.
Also, you shouldn't shoot a lot of .22LR through a sealed (non-serviceable) can, like mine, because of the buildup that can occur from .22LR ammo (it is really dirty). You can get a reasonable .223 can starting around $550, + the $200 tax stamp and a 6 month wait. 7.62 cans start at about $700 and go upwards of $1,200, plus the $200 stamp. My can, stamp included, was just over $1,000.
You would be better off ordering a .22LR dedicated can for your pistol and rifle that you can clean. I had my dealer set aside a Gemtech Alpine today. It can handle .22LR, .22 Mag, and .17 HMR. About $350, plus the stamp.
Final can will be one in .45ACP. That way I can use it on my .45ACP pistols, and lesser calibers. Good pistol cans start around $700.
3 cans will pretty much cover all of my firearms that have threaded barrels. Better to buy a higher end can, as you will likely own it for the rest of your life.
I formed a specific NFA trust so that other trustees in my trust can use them without me there. My wife, boys, dad & father-in-law, and one friend are listed as trustees. If I owned them in my personal name, no-one else, other than a class 3 dealer, could have them in their possession, and that would cause an issue when I die, making my heirs go through the transfer process, and pay a $200 stamp fee for something I already own.
Hope this helps.