44 Spl suppressed can certainly be an interesting option. One thing to know though - generally speaking the bigger bores are a bit louder, both sound of the suppressed shot and sound of the bullet in flight, as well as much louder sound of impact which can actually be pretty loud in some circumstances. While the difference doesn't seem to be significant to my ears between 30 and 35 cals, perhaps because a small volume 38 Spl or 9mm does the job with a lot less powder than 300 Blk, I can definitely tell the difference with 44 and 45 cal stuff, enough to the point that if I want something with the ideal blend of terminal effect and quietness I prefer a 35 cal with some sort of lead hollow point designed for low velocity expansion.
Sometimes people look at the low velocity numbers of cartidges like 44 Spl and 45 Auto and expect that will naturally make them quiet, but avoiding supersonic crack is only one part of the sound signature and the bigger stuff just makes more noise at the suppressor and downrange. Bullet weight plays a big role in the sound down range too, which is one reason I like the 35 caliber stuff to suppress; I can use a little 90gr solid for very quiet small game loads that hardly make any noise, or go all the way up to 250-300gr heavies depending on the twist rate for use on larger game. I fabricated a 255gr hollow point mold that works in a bunch of different 35 cals (too big for the 9mm, but works in 38/357 up through the bigger 35 cal rifles) and has been very successful on chunky southern whitetail, but for quieter plinking I generally stick with something a bit lighter weight. As Cascade Hemi mentioned above the 38 Spl bullets can be had dirt cheap if you don't cast your own, so that's an advantage too.
But your use case may be very different than mine; I rarely shoot at any sort of public range or organized shoots, mostly shoot out in the woods or hunt so the difference in sound levels can be much more significant than shooting with a bunch of other people and gunshots around. Of course if one wants to take the sound level part of this to the extreme while sacrificing terminal effect, there's bolt action or single shot 22 LR options that can be incredibly quiet. Or go the other way with the big bores and sacrifice sound in favor of terminal effect, which is where a 44 Spl can shine if you're taking bigger game with it - there's no wrong answers, just a sliding scale to look at and determine what fits best for your application. And of course there is a right answer - get one of each, and a whole bunch of suppressors to match, then circle back and get more of each.
