Any decent factory ammo will be fine. If using factory ammo I use Federal American Eagle 240 grain hollow points. You can pay more but you won't get significantly better deer ammo. A lot of guys like to use cast bullets for hunting (me included), so I load my own. This is certainly not necessary. Ammo loaded with Horady XTP bullets is bound to be good too, but again it's not really necessary. The 44 magnum kills by making a big leaky hole and penetrating deeply.
100 yards is realistic with practice. I get 4 inch groups with my 629 and 100 yards with a 2x scope. It takes quite a bit of practice to be able to do that consistently, so plan on shooting at least a few hundred rounds.
I consider 100 yards a long shot with a 44 magnum revolver, and I prefer to keep shots within 50 yards if possible. For one thing, bullet drop due to trajectory is a big factor beyond 100 yards so if you estimate 100 yards and the deer is really at 125 yards, then you might miss or wound.
The key thing with handgun hunting is to always use a good rest.
Do not use the 180 grain bullets for hunting. For one thing, the muzzle flash can be blinding in dim light and for another thing, the extra penetration of the 240 grainers is a good thing.