They're all about the same power, they all get to 62mph in 9.x secs, so it just depends on what you want it for: B road blasting, boulevard cruising, motorway cruising?
The best handling (lightest) will be the 1.8T and it will be the most tunable: the 2.4 is utterly beyond help unless you're spending several grand, in which case you would be better off with a 3.0 V6.
The most economical will be the 2.5TDI and due to the torque of the TDI may actually feel the fastest once you're off the line: mpg in the high 30's, 1.8T will be around 30 and the 2.4 will be mid to high 20's.
The only thing really going for the 2.4 is that it's a V6 petrol, so will sound better.
My preference out of those would definitely be the 1.8T because it's the only one that's available in quattro
And regardless or FWD/quattro, because if I got bored and wanted more power, it is the easiest to tune up cheaply: both the 2.5TDI and 1.8T will get around 175-180bhp with a standard remap, so without too much stress (effort wise or on the components) and the 1.8T can go way beyond that if you wish to push it, the 2.5TDI's torquey power delivery makes it unsuitable for putting too much extra power through the front wheels, while the 1.8T could probably handle 220bhp territory (with a few mods in addition to the remap!) without overwhelming the front wheels.
IF you can find one, consider a quattro: the torsen differential is a much more direct 4WD than your S3 (unless you've had the Haldex modified to keep it in/close to 4WD the whole time).