Ok so now lets talk optics. Red dot? Small Scope? Iron sights?
44mag is 150 yards or less for deer catridge imo.
So with that being said.
Open sights are the most period correct but the least accurate option. Also as you get closer to
@"J" in age you might find it hard or impossible to focus on the front sight post AND the deer.
A good peep and post can be scary accurate and fast.
Red dot is another good option, the sig and vortex options start around $100 and go up from there, or get an aimpoint if you feel the need to drop that sort of coin on a hunting gun.
If you want to go scoped (and i don't blame you, my centerfire ones have been scoped) go low power fixed or lvpo. I really like my 1.25-4 Leupold with the red dot in them. Plenty of zoom for the range but 1.25 is close to a red dot when stalking for quick shots. I have one on my muzzy that I'll have at salt fork if you want to look through it.