Congratulations on your first Antique Barnes.
S&W #3 .44 Russian .... Oh Yeah !.
My 44 is an RR in .44Special. Uses the same bullet dia. as your Russian (.430-.432")
If you slug your bore and throats, size the bullets to 1 thou. over throat dia., it'll pay off in improved accuracy.
Have become rather fond of this mold: Lyman 429244DV. It's a SWC, GC, four holer, that drops soft lead at .432" and 265 grains. I use them unsized and sans GC, tumble lubed ... no problem. Capable of 2 inches at 25 yards(if only I could hold it so well!).
Have also become fond of Alliant 2400 powder. Its a very progressive slow burner. Bulky, theres no chance of a double charge escaping your notice. Dirty burning at antique pressures?, most assuredly yes ... but there are no surprises as one slowly increases the charge to what your revolver is comfortable with. Just ignore all the fluff in the bore.
2400's gentle pressure curve allow's one to safely utilize the most vel. that is prudent in the old girls. Thats important to those of us who spend time in deep wilderness.
A chronograph is indespensable if one wishes to develop loads much steamier than squib/target levels, IMO.
2400 has proven safe up to original BP speeds, or a wee bit more

, without undue strain to my precious 'ol girls.