Since all 357 guns can also shoot 38Special and 38Spl+P, that's the flexible option.
In a real SAA, "true clone" or "near clone", there's not enough power for the 44Magnum. Hot-rodded 45LC+P rounds exist but those are only for guns that are also available as 44Mags. So your net power available in 357 is higher than in 45LC. 357Mag SAA types are a bit heavier than 45LCs due to the extra metal in the cylinders and barrel walls.
The 44-40 is tricky because it's supposed to be .427 diameter, whereas the 44Russian/Special/Magnum family calibers are .429. So a LOT of "44-40" guns get shipped with .429 barrels and sometimes an extra cylinder in 44Special.
In which case you either have to reload with .429 components or find a supplier of "mutant" 44-40. Which are available if you search, but it will cost you.
The next problem with 44-40 is that as a bottleneck cartridge, it's more difficult for a newbie to reload for. Not THAT bad mind you but it is more difficult.
Personally, if I'm going to go with an old-West oddball bottleneck round, I'd look to the 38-40. It's bore is genuinely identical to the 10mm and 40S&W so bullet components are easy to get. Ballistics of the 38-40 are nearly identical to the 40S&W. A special-order double-cylinder gun in 38-40 and 40S&W would be WAY cool.
Bottleneck cartridges are really neat in SAA type guns as they insert into the chambers faster and easier, and in the case of the 38-40 and 44-40 operate at low pressure so they usually fall right out of the cylinder bores. No ejector rop needed, just get the loading gate open, tip the barrel up and spin the cylinder along your arm. Major style points
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Which brings us back to the 357Mag. Two more modern bottleneck cartridges with the benefits involved exist but fire .357 diameter bullets: the 356GNR (using a 41Magnum shell necked down to 357) and the 38/44Bain&Davis (same concept starting with the 44Mag and necking it down). In an SAA or similar you could NOT safely exceed 357Magnum power levels (meaning bullet speed for a given weight) but you drop the pressure from the bigger case and you get the easy feeding/extraction issues, esp. if you run them at lower power. A 38/44B&D shooting a 158gr lead load at 1,000fps would be a real sweetheart and an effective street defense piece.
For these calibers, what you do is, you buy a 357 gun and get a second 357Magnum cylinder. Get the second cylinder properly fitted by a local gunsmith first if need be, do what it takes to make it shoot well, and then send the cylinder alone off to a gunsmith for modding. If you're going for 356GNR you send it to Gary Reeder. He can also supply new brass, loading dies and reloading data. You'd need somebody else to do a 38/44...don't know who but let us know if you're interested...I'm mildly so and have done a bit of research. Either way, the cool part is, when you want to swap back to standard 357Mag the other cylinder is right there.
I own a Ruger New Vaquero in 357, a "near clone" of the SAA. It's about as strong, almost identical in size and feel, fits the same holsters but has a modern transfer bar safety so it can be carried fully loaded just like a modern DA revolver. The Beretta Stampede and Taurus Gaucho are identical in concept: "transfer bar equipped SAA near-clones". I think Ruger's version is the best
. Especially if you're going to modify it - the New Vaqueros can parts-swap with a lot of other Ruger SA guns. Mine has a SuperBlackHawk lower hammer and improved sights...plus I added a bit of..."psychological warfare"
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The earlier Ruger Vaqueros looked similar but were built on a larger 44Magnum-class frame. They don't feel like an SAA.
If you REALLY want a gun lacking a transfer bar or other modern safety, OK, buy one. But I'm not sure I'd recommend it for a newbie shooter and the plain fact is, I didn't trust myself with one.