I shot Specials and Russians through my .44 Specials - and my 629MG. I finally ordered a Hogue backstrap-enclosing .500 Magnum grip from S&W, the only current source ($35). They made the difference - I could shoot 'real' Magnums without severe pain. I bought a new 6" half lug 629 just to use that grip - great pair. Ultimately, I replaced my 629MG with a new standard 4" 629, identical to the 6", just shorter. These new 629's both sport those .500 Magnum Hogue grips and are 'real' .44 Magnums, when needed. Other times, they are perfect for .44 Specials and Russians, too. You must clean the chambers between short cases (Specials and Russians) and Magnums, of course. If you have to have a .44 Magnum, either is a great place to start. You can buy 'mild' .44 Magnums in the guise of 'Cowboy' ammo from smaller ammo makers, like Georgia Arms.
Now for another choice. How about a more frugal on both the pocketbook and wrist big bore? Try a 4" or 5" 625 - or the best value, a 625JM, in .45 ACP. You can buy a box of fifty for little more than .38 Special plinkers - at Wally World - on Sunday. .45 ACP ammo is everywhere... try to find .44 Russian or Special (I have loads... but I reload!).The recoil is easily handled by most, but you could always add those aforementioned Hogue .500 Magnum grips to ease it even more. The muzzle stays down, as the full lug adds an ounce or two over that 4" 629. Check the S&W website, that 625JM really is a bargain for the gold bead Patridge sight, much less it's easily changed design (Most other S&W front sights are pinned.). The Miculek stock is pricey, too... if you like it, the 625JM becomes a great value. Of course, it'll take any .45 ACP round - in a moonclip, for super-fast reloading. Great way to ease into a big bore.
Stainz
PS Those Hogue made-for-S&W .460/.500 Magnum backstrap enclosing and recoil absorbing grips are on all .460 & .500 Magnums. One size fits all: K, L, N, or X-frames.