I just went through this. It can be an obsession if you have a bunch of different weapons and platforms. I wholeheartedly recommend getting at least 1 .22 can with your first purchase. They're cheap and a blast to play with. With my kids, it's a must at this point.
Your best bet is a good 30cal can for your 7mm. I went with a AB Raptor 10 in 7.62 with a 3" reflex and an AB Little Bird (.22). About 100 days into that wait, modern warriors had a sale and I picked up a CGS Hydra (.22), and a YHM R9.
My last two cans got approved first at 112 days and my ABs got approved at 256 days roughly 2 weeks later. Both were approved in pairs. The only given is that if you're even thinking about it, there's no better time to get your paperwork in than yesterday.
I bought all of mine through online vendors who transfered them to a local FFL who has a silencer shop kisok in his store. I did all of my paperwork through silencer shop online and did the finger prints at the kiosk. I did a single shot trust on all of them. I'd recommend that 100%.
If you're hunting with it, a titanium can that's as short as possible with the level of sound suppression you want. After all of my research, the AB Raptor seemed to be the best for my needs. There are tons of YouTube videos and reviews all over the internet.
Otter Creek Labs, Dilligent Defense, TBAC, CGS, and AB all likely have cans that will suit you but you need to dive in to see what you're really wanting.
My Raptor is by far my quietest can but my YHM R9 might be my favorite because it's so versatile. I can swap it from my 300blk, to my .308, to my 30-30, and then to my 9mm pistol. It's perfect for the range and just messing around and has very respectable decibel reduction on all. My 30-30 with my subsonic loads is ridiculous.
Skip the QD BS right now and just focus on direct thread. If you research like me, that will save you at least a week or two of pounding your head against the wall. With that said, I find it important to have a can that has the universal HUB thread pitch so it doesn't lock you down to a specific type of mount in the future.
There, that's about all I've learned in the past year on the subject. I have 4 now, covering almost all of my bases buy I imagine I'll be putting in some paperwork for a 5th shortly. I want to try a Dilligent Defense or OCL can.