Hard one to answer,
I concur with gent above, 44 mag is best kept to 100-125 yards, but mostly because of trajectory, it keeps energy fairly well beyond that. Real issue comes down to what bullet your barrel will shoot accurately. My experience with Thompson Center barrels is that they won't shoot light bullets all that well, generally mine have liked 240 grains and better (I've had 2, 10 and 14 inch). The most accurate bullets in either of my barrels have been the 300 grain cast flatnoses with gas checks. I hope you have luck with your 44 adventure, I have heard of others on this post having success with 180 grain jacketed pill, but I never had an great luck with the accuracy of them in my barrels. I have a custom VVCG stainless 10 inch 44 on the way, maybe it will shoot the lighter bullets?
regards,
Graycg