44 Mag is a good hunting round, will do whitetale with out too much damage. I prefer a 41 mag, but you will need to handload to get the most from this caliber. Also a 357 can be effective but probably not over 75 yds, and shot placement is even more critical.
As others will tell you, start small and work up: 22, 38 spcl, 357 mag, and then 44 mag. Sounds as if you have done this important step. This will reduce the potential for developing a flinch.
Single action vs. double action? Personal preference, I recommend shooting both before plunking down the money.
As far as the red dot sight goes, they are ok for other than dusk and dawn. If it is a low light application you will do better with an optical scope (2 or 4 power).