A new 4" 629, or a 6" if you like the extra length, will be difficult to beat for all normal SAAMI loads. Don't let folks fool you, the originators of the .44 Magnum know how to make a revolver stout enough for a diet of .44 Magnums. They will have a better trigger, post break-in, than any Ruger SRH/RH. And... don't let folks fool you, Redhawks have a funky trigger - the Super Redhawk has a trigger that is far more capable, although still not in the S&W ballpark. And... a 4" 629 weighs less than a SRH 'Alaskan' snubby, while the 6" 629 weighs 3.5 oz less than a 5.5" Redhawk. The 4" & 6" 629's share the same sights, half-lug design, hammer, and trigger. Fitted with the backstrap-enclosing S&W .500 Magnum grip by Hogue, a $35 goodie only available from S&W Accessories, they are quite comfortable to shoot, too.
If you need a longer, say 7.5", barrel - and you want to 'scope it, a SRH may just be the ticket. If you need to shoot super-hot loads, perhaps a larger caliber, the .480 Ruger or .454 Casull, for example, is more appropriate. I owned a .454 SRH for years before getting my first 629, a Mountain Gun, some four years back. I still have a 5.5" .45 Colt Redhawk. I have shot other examples of both. I still have two 625MG's in .45 Colt - which have better triggers AND group better than either of my RH/SRH's - with the same .45 Colts (That SRH was a tackdriver with .454's!).
Note I have suggested DA capable revolvers. If you need to use it quickly, nothing beats a DA revolver. If it will NEVER need to be used in an emergency, a SA may be adequate - I have an assortment of those. The 4.6" SS Super Blackhawk is a handy, albeit heavy, size (It weighs a half ounce less than my 6" 629!). I fitted mine with a Bird's Head Grip, which is an acquired taste with hot loads. The original BH-like grip of the SBH is fine for many folks - and rubber aftermarket grips exist.
Again, for a first - or only - .44 Magnum, I'd get a 4" or 6" S&W 629... and save $35 for those grips.
Stainz
PS About S&W vs Ruger... remember, S&W's are forged and heat-treated, Rugers use cast steel - they require more mass for the same relative strength. Their solid frame vs the removeable sideplate of S&W's is a plus, however. Either will serve you well.