Of the choices, .44. But, you COULD get you a new gun in .308 or something, you know. I have stoppers up to 7mm Rem Mag and my .308 is my fave for deer, stops 'em right now with limited meat damage. I shoot a 150 grain Ballistic Tip. There's more choices than THAT, though, everything from .243 up to anything above that. There's no such thing as "overkill" on a deer.
Lots of folks claim the .223 is enough and I've taken one deer with my M4. Yeah, it worked, but he went 20 yards before dropping with a hole in its heart. But that was a sample size of one, so I was impressed enough. But, I see no reason to routinely play with pop guns when one can use a DEER RIFLE. And, I'm not that crazy over MSRs. I don't mind my bolt guns. Deer hunting is not a contest of firepower and what you're wanting is HORSE power.
I have traditional Savage 110 and two Remington bolt guns, may not be tacticool, but it sure gets the job done. I still hunt with that M4, makes a GREAT turkey gun and I could get a more appropriate caliber upper for it, but why? .308 is a pretty awesome deer getter.
But, sounds like you're not wanting to buy something, just playing with what you have. So, yeah, .44.