Which South hand fits the bidding best?

Solution

First: is North's 2♠ bid game forcing or forcing for one round only? The answer depends on NS's bidding system:
- Classically 2♣ is game forcing (since the 2♥ and 2♠ openings – and perhaps also the 2♦ opening – are strong, 'semiforcing').
- However, most pairs nowadays play only one strong opening: 2♣. All other two level openings are weak (Weak Two, Multicoloured, Tartan, etc.). They play North's 2♠ bid only one round forcing.
In that case there is one (and only one) bidding sequence that allows NS to stop below game: if South now bids the cheapest suit (not notrump) – in this case 3♣ – a so-called second negative, and North repeats his suit – in this case 3♠. Any other bid by either North or South makes the bidding game forcing.

South 1 should bid 3♠ – game forcing, even if 2♠ may be only semiforcing – because he is too strong (!) to jump to 4♠. North has claimed to make (almost) game on his hand alone. Therefore South 1 is interested in a slam, especially if North has a game forcing hand (if he has the slightly weaker semiforcing hand, he will have to 'apply the breaks' sooner or later).
Why does South 1's 3♠ bid show a stronger hand than a leap to 4♠ would (this is called The Principle of Fast Arrival)? Because the 3♠ bid saves bidding space: it allows NS to start showing controls below game level.  

South 2 should bid 3♠ ('Slow Arrival') as well. The same reasoning applies as with South 1. In view of his good hand South 2 considers a slam and tells his partner so by bidding 3♠.
(If NS have agreed upon Splinter, South 2 may consider jumping to 4♦ over 2♠: a slam try, establishing spades and showing a singleton or void in diamonds. However, according to many experts South should have four trumps to do so. Something to discuss with partner.)

South 3 should bid 4♠, a 'Fast Arrival' bid. So this is the hand that fits the bidding best.
North's 2♠ bid means: 'I can (almost) make game myself.' By bidding that game at once – thus taking away bidding space – South 3 conveys the message: 'As far as I am concerned, we cannot make a slam. I have a (small) spade fit but little or nothing extra.' Unless North can make (almost) twelve tricks in his hand alone, he will pass now. 

(A somewhat more detailed agreement: if South has an absolutely useless hand – let's say a flat hand with three spades and 0-2 points – he bids a 'second negative' 3♣ over North's 2♠. Especially if North can have a semiforcing 2♣, since South can subsequently pass North's 3♠ bid.
A consequence of this is, that a direct leap to 4♠ over 2♠ now does show 'something' (but still not a lot: at most one second round control). South 3's hand is very suited for such a leap.)