Of those powders, I would choose Power Pistol as the "safest" choice. Bullseye in .357 makes me nervous since the small charge in that long, skinny case would be easy to double-charge without being completely obvious. The results of that would almost certainly be catastrophic. If you visually inspect every charge carefully, no doubt you'd see it, but Bullseye would be the easiest to overlook. By my calculations, a double charge of PP would not overflow the case, but it would be so full I don't think you could seat the bullet (using 158 gr. JHP data).
4227 would also be safe since it doesn't seem to have a rep for squibs, even if downloaded (within published data). It's also impossible to put in a dangerously large charge and still seat a bullet (for a magnum revolver...maybe you could damage a .38 Special with a full case of 4227). 4227 would be the least efficient (in term of velocity you get per grain of powder) and would probably be a poor choice for light bullets. I've never seen it recommended for bullets that are not at least mid-weight for the caliber. I've only used it with magnum primers, so don't know if it would be inconsistent with standards. I'd only choose it today if you are hoarding the Power Pistol to use in some other caliber, or you don't want to see the bright white flash of PP (or H110/296). You'll see almost no flash from 4227, in my experience.
edit: Oops, I see Hodgdon does have data for all bullet weights in .357 Mag with H4227. I guess I just payed it no mind before. Maybe I'll try some 125s with it in my lever gun some day, if I get bored with all other possible combinations.