Loads of great advice!
I would just like to add that if you've been playing the Alto a while you shouldn't find getting your embouchure a bit tightier for the Soprano. Its such a tiny mouthpiece that requires a nice tight seal! Apart from that its learning to control the intonation of the Sop will help your Alto playing no end!
Shape is a personal thing but I wanted a straight sop for something a little different to my Alto and Tenor! I'm lucky that I have a straight and curved crook, much prefferring the latter which helps holding the sop at 45 deg rather than 90 deg out of my mouth ;}
I don't use a strap as that actually made things harder for me. Initially your right arm will struggle but like anything else you'll get used to it very quickly.
I find the curved sop's freakishly small :shocked:
Like every other sax, good luck with the mouthpiece hunt! it can change everything

))
Check out Greg Vail with the Sop here to see how a curved crook changes how you hold the sop!