It is very important when it comes to airgun silence to make a distinction between spring piston and PCP (pre charged pneumatic) models.
With spring piston I also mean gas piston guns (which IMO are nothing but a marketing hype). Spring piston guns do benefit from a silencer, even though you will always have quite a bit of noise from the piston slamming home.
When choosing a quit spring piston gun do not go for the most powerful model if you want something silent. If it is your first or only airgun I would also not buy a powerful spring piston one either. With powerful I mean spring guns that generate over 22Ftlbs, 18-20 FtLbs is plenty for target shooting up to 40 yards. Good brands / models to consider are: Weihrauch HW 77, 97, 95. Diana 34, Airarms etc. Or even the Ruger copy of the Diana model 34 is meant to be decent. CZ also makes great beginner guns. You could even consider a second hand match spring piston rifle, for example a Feinwerkbau 300. Try to stay away from brands such Gamo and Hatsan and other Chinese, Turkish, Spanish and Mexican guns (and their rebranded versions). They IMO make over marketed rubbish that give spring guns in general a bad name.
PCP’s will be even quieter than a silenced subsonic .22 rim fire, I have tons experience in shooting both. A good PCP will allow to you shoot one hole groups at 50 year easily. They have no vibration, even less recoil than a .22 rim fire and many are multi shot. They are powerful enough to take down most small game. Brands / models to consider are CZ or the BSA Lonestar (if you are on a budget, and even if you are not they are still great guns), Weihrauch, Steyr(second hand) etc. I would stay away from brands such as Airforce, Korean brands etc . unless you want to spend a lot of money and time on tuning them. I would also avoid overhyped & overpriced brands such as Daystate, Ripley, Theoben unless you can get a good second hand deal.
Many PCP’s will easily generate between 30 and 40 Ftlbs. A spring gun at these power levels would make a lot of noise (even with a silencer) and would be hard to control. The more power a PCP has the less shots you get between fills, this is something to consider depending on whether it is mainly going to be a hunter or a target shooter.
A PCP would be my first choice for backyard shooting up to 50 yards. Complete silence ( your bullet trap will make more noise), dead on accurate and cost saving in the long run ( or short depending on how much you shoot
).
Of course there are things such .50( and bigger) call PCP’s but for obvious reasons I have left these exotics out. There are also CO2 guns but unless you plan on bulk filling I would not consider them, as most CO2 cartridge guns are not what I would consider serious adult airguns. But if you want to shoot at short distances and do not want to hunt a second hand match (Anshutz, Walter, Steyr, Feinwerkbau etc) CO2 gun might be the way to go as these guns can often be purchased for very little money. There is also pre compressed air which in the past was very popular with match airguns, and which you now mainly find with some (cheaper ) airpistols.
Anyway I hope that this helps.