Slufoot: it almost totally depends on the particular rifle you have and its twist. If you have a marlin with the micro-groove barrel you will want to lap the bore, ala Veral Smith, to get cast, gas-checked bullets to shoot accurately. I have lapped the bores on a couple of 444s, as Veral recommends, to .432", load them with 300 gn or 330 gn cast gas checked bullets from Beartooth Bullets (I would call the owner a desciple of Veral) over Varget or H322 for groups of an inch or less at 100yds.
I use H4198 when shooting jacketed 240s. Hodgedons powder gives loading data on the powder cannister labels for their powders and their formula for the 444 and 240 gn slug is way more accurate than any factory load I have thrown down the tube.
Now, since you are loading the 444, hie yourself on over to the Beartooth Bullet website and read the owner's treatise on the 444 and review his load data. As mentioned earlier, he is a desciple of Veral Smith and his accuracy results with the 444 are incredible. HTH. Mikey.