9x57 sounds cool and if you were buying a classic rifle I'd go that.
But you're reboring and I'd give it a miss on those grounds.
Those .356" cal pills aren't easy to get.
If you're aiming for something easy to load I'd recommend a 358 Win more and I prefer 57mm rounds so that's an indication of how much the RWS pills cost and how hard they are to buy.
I don't know about S&B but it's an oddball outside Europe and that's what counts when you're trying to feed it.
338x57 is again a bit of a fiddly choice.
Again, I prefer 57mm cases, but 338 Fed has had some success and is available and effective......why re-invent the wheel?
Of the others 9.3x57 seems the best.
There are a wide range of bullets, the cheapest being the 270gr Speer Semi Spitzer, and it's a good round.
But if you're thinking about that cal why not see if you can fit 9.3x62 into the mag?
It's the same case head, 1mm shorter than an '06 case and they fit into a 8x57 mag.
The cases are made by Lapua and are good - I should know; I own a Tikka T3 in this chambering and it's great.
I guess what I'm saying is think about which will be most effective.
Don't make extra trouble for yourself if you don't have to.
And if you do take the extra step and go a 9.3x62 you won't look back.
It was designed as a cartridge for German farmers in Africa who needed to feed their family on antelope and bok of any description but would also be powerful enough with a well placed shot to take any dangerous game up to and including elephant.
You will find it in your hand much more often than you suspect, expecially if it's a in a light to medium weight rifle.