Guns & Ammo (current issue) has a pretty good article about handgun hunting. One of the interresting things pointed out is the importance of range restriction especially on iron sighted handguns. Since the iron sights can completely obscure the vitals of a deer at 100 yards, it can make precise shot placement tricky.
Ballistically a 240 grain .44 mag bullet will have no problem taking a deer. Even the 180 grain will work. Just use a properly constructed bullet. Shoot what you are most comfortable with. The 240 grain bullets will generate more recoil than the 180s.
As with all other game, bullet placement is key. It doesn't matter if you have too much gun, a poorly placed shot is going to loose game. An accurate 180 grain to the vitals will prove more effective than a 240 grain launched into the gut.
For getting a lot of practice in and still keeping your teeth in your head, I'd recommend shooting some very mild loads. This will get you used to the feel without developing bad habits induced from the recoil. I've been doing a lot of practicing with my .44 shooting 240 grain HCL bullets over (IIRC) 6.x grains of red dot. This gives a felt recoil of about that of a .38 special. These are super cheap rounds to reload. The brass lasts for about forever if you don't over crimp, bullets run around $30/500, and at 6-7 grains a charge, one pound of powder lasts a while.
If you don't reload, look for some CAS (Cowboy Action) loads. These are pretty much the same loading, although they can be expensive.
Lead fouling can be pretty bad, however. What I do to make cleanup a lot easier is to fire a cylinder of jacketed rounds at the end of a session while the barrel is still warm from the naked lead loads. This helps to clean out a lot of the lead deposits.
As for what factory load shoots best, that is anybody's guess as each gun shoots different. Try some various loads out and see which one(s) your firearm prefers. All that shooting makes for good practice too. /ubbthreads/images/graemlins/smile.gif