Having owned a 629 4" Mountain a couple 6" 629s a 4" 629 and a 5 1/2" stainless Ruger Redhawk and in shooting a couple different classic 629s a few of my observations are as follows.
The 629 Mountain is a sweet carrying pistol it is light and handy is the best option of your choices listed if the pistol is to be carried allot and not often shot (with full loads) used as a just in case something decides try to eat you as its happy meal gun.
Full power heavy loads can grow tiring after a short while the recoil comes back into the web of the hand noticeably a little more than any of the other choices listed.
The 4 inch standard 629 has a great balance of power and ergonomics it clears leather fast and points well and balances well and out to 100 yards does as well as the 6 inch barrel for me.
The 6" 629 is more of a hunting handgun it carries better in a shoulder holster than on a belt whereas the 4" models work well on a belt or a shoulder holster and are always handy.
The 5" Classic has the balance or weight more forward it helps to soak up some of the recoil but if I have to carry the weight I would rather have the extra inch of barrel with a 6" 629 with its longer sight radius and increase of velocity over the heavier 629 classic's 5" lugged barrel, if recoil bothers you then you could have a 4" or 6" pistol magnaported or something similar.
The Ruger Redhawk is (IMO overly) heavy with the weight noticeable more in the frame it is massive compared to the 629 Mountain or 4" 629 this weight is noticeable after a long hot summer day of carrying it all over.
I soon went back to my Smiths for a couple different reasons.
The Rugers trigger pull never was near what any of my S&W's were despite stoning the action and replacing the springs.
I never cared for the Ruger's ejector rod it always seemed loose and fragile as it wobbled a bit.
On the S&W its butter smooth each and every time always clearing even the stubbornest of handloads.
The Ruger's balance for me is all wrong and the weight seemed to be in the wrong places much of it needlessly so, it ended up being sold.
IIRC the Ruger is made from castings and the Smith & Wesson is made from forged steel.
Accuracy wise any of my S&W's .44s could and did beat the .44 Ruger time and again.
Elmer Keith had it right a 4" S&W .44 Magnum 29 or 629 is one of the handiest pistols to have around should the need arise.
Not trying to start a flame war as these are my opinions others have theirs but as for me a 4" 629 standard fits most of my big bore centerfire pistol needs.
Good luck on your search, mine took nearly 30 years in the end the 4 inch standard 29/629 is my favorite of the .44s followed by the 4" 629 Mountain as its better to have it and not need it than need it and not have it.
Any 4" .44 is hard to beat as a field pistol especially if you get into or are into handloading.