Hi Erik,
I have a SBH .44 with a 5-1/2" bbl and love it. It shoots tight groups and is easy to carry. I did have a trigger job done, and had adjustable Millett sights put on it to help out my eyes. The trigger job was not expensive, and did wonders for lowering and crisping up the pull. I don't do primary handgun hunting with it, but do carry it as a backup when shotgun or rifle hunting in a western style rig. With iron sights, I don't trust my eyes for shooting beyond maybe 50 yds. That's why I don't use it as a primary handgun hunting pistol. If I am handgun hunting, I use a scoped SRH .480.
You indicated you are looking at a 7-1/2" barrel? The extra weight and length will improve control and accuracy, but it is a bit long for easy carry on your hip. If you are looking at the Hunter model that has the barrel rib with scope mount cutouts, that would make an excellent pistol for handgun hunting. Put a red dot or a 2X scope on it and as long as you do your part, you should be good for 100-125 yds with good ammo. If you go that route, Pistol Packaging makes a nice bandoleer holster for cross draw with cartridge loops. That's what I have for my SRH .480.
You may want to put a set of after market grips on it. I found the stock grips a little small for my hands. The dealer had already put on Lett faux ivory grips on the one I ended up buying. They are just slightly more hand filling than the stock ones. The only time I found recoil an issue was if I took a high hold on the grips. Then, as the gun comes back, it tends to whack your middle finger with the back of the trigger guard. I moved to a lower hold and have had no trouble since. I shoot everything from factory 180/240s to Corbon 265 HPs and their bigger hard cast thumpers, and my own handloads.
The Ruger SBH may not be the most incredible handgun made, and certainly is not in the class of an FA or a Bowen custom job. But, it also takes a much smaller chunk out of your wallet. I have been extremely happy with my SBH and SRH. They are definite keepers.
Good luck and happy shooting.