Good question,
All I hunt with anymore is Marshall's cast bullets. If I were going out hunting whitetails with factory loads, I'd use one of the following for 44 mag...
300 gr Federal Cast Core
270 gr Speer (plated bullet) Also loaded by Buffalo Bore I think
240 (or 250) gr Federal Hydro Shok
265 gr Remington (It's their Golden Saber bullet with a different name for their hunting line)
300 gr Hornady XTP
There are probaby a dozen or more excellent factory loads for mixing the 44 mag with deer but these are the ones (bullets, not factory loads themselves) I have some experience with. I'd probably prefer them in the order I have listed but that's more guess than fact. Heavier bullets usually mean more recoil while lighter bullets make more noise. Find a load you & the gun like and have fun.
The other (and better option I think) option is to get started in handloading. It's tons of fun. Let us know what you end up with.
God bless................... Bill M