Lots of questions to answer and some answers will end up being your personal preference. That being said, I like to hunt with both iron sights as well as scoped revolvers. I prefer the Rugers, they are built strong and accurate. With a little work they can be extremely accurate but some gun smithing would be needed. You can do the work yourself if your semi handy. A little attention the the chamber throats as well as the forcing cone along with a lighter trigger spring kit and you're in business!
The .44mag is suitable for pretty much any North American animal and THEN some. Sure there are the ultra mag big bore calibers out there that can do a better job (.460, .454, .480,.500 S&W Mag, etc...) but the .44 is PLENTY gun for the task at hand.
I like to keep my shots under 100yards with a scope, under 50yds with adjustable iron sights and under 35yards with fixed iron sights. That's just me...your mileage may vary.
You can see just fine through the scope at arms length, they are made for this as they areEER scopes, (Extended Eye Relief) and you should have no problem picking up amoving target as you described. Go to a shop that has one mounted and give it a try, you will see what I'm talking about. Variable scopes are fine but a bit overkill for a revolver if you ask me. I like the simplicity of a fixed scope and since I keep my shots under 100 yards, there is no need for further magnification. If you plan on shooting at greater distances than a variable scope may be the ticket.
Barrel length is also subjective, you can pretty much use anything from a 4in barrel up to a 10in barrel on a revolver and you won't see too much difference as a hunting tool. I prefer 5 1/2in to 7 1/2in for barrel length as that just seems to balance best in my hands. I do like the smaller barrels for trail guns as they pack easier and still have a punch.
As far as hunting with a pistol, it's an absolute blast and a challenge too. You will find it very rewarding.
This is was my primary hunting pistol this year, it's a .44mag Ruger Super Blackhawk Hunter with a Leupold FX-IV scope:
I've also hunted with this .44mag Ruger Vaquero with fixed sights
I killed this deer with it. The gun is on my right hip under my shirt, you can just make it out. This was my first buck with a pistol because up until a couple years ago Illinois would only let you hunt with a pistol in the late antler less only gun season. Now you can use it during the main gun seasons...I was stoked!
I've also hunted with all of these revolvers as well.
Top to bottom:
Ruger Super Blackhawk .44mag (With 2x Leupold)
Ruger Vaquero .45 Colt
Magnum Research BFR .454 casull
Ruger Blackhawk .45 Colt
This Ruger Sheriff .45 Colt makes for a great packing gun and when loaded up it will take down anything the.44mag will.
Hope this helped some.....