.44 Mag? That has always been a cast bullet round, as far as I was ever concerned. Never even considered jacketed bullets--too expensive when cast works so well.
240gn L-SWC has always been the first choice and, for many, the only choice.
If hunting thin skin game, you can try 180-200gn XTP or JHP.
I would not even consider a plated bullet. All that I have ever tried were absolute garbage in the accuracy department and, with the high cost of these "bullets" now, a jacketed bullet would be much better.
Montana Gold has an excellent 240gn JSP for $333/1950 or 17 cents a bullet (where most jacketed bullets from the big names seem to be about 24 cents each).
Penn Bullets has 240gn L-SWC and L-TC for $105/1000, or 10.5 cents a bullet and matercastbullets.com has 240gn L-SWC bullets for $92.57/1000 and 300gn L-GP bullets for $57.85/500.