Welcome to THR, lots of great people here
Lots of powders will work but you are looking at 2 most likely 3 flavors
Rifle-223, pistol 9mm .357, .44, .45, mag pistol-full power .357, .44
Multiple choices for each so it may be a matter of what you can find
I like
.223 TAC, BLC(2), 8208, H335
9mm WSF, CFE-P, BE86, Silhouette
.357 light-med, HP38, BE86
.357 Full power H110/W296
.45 HP38/W231, AA#2 (WSF, BE86, CFE-P would also work here)
Don't own a .44
You could do all the pistol rounds with one powder (assuming you don't want full power loads in the .357 and .44)
HP38/W231, CFE-P, BE86, Universal, Unique would all be good choices if you want to try to do all the pistol rounds with one powder
If you are checking manuals you will see Titegroup listed for all 4 pistol rounds, lots of people like it, I don't care for it, but it is not a good choice for a beginning reloader IMO, small charge range and not forgiving