AMK or BAM engine, if yours isnt a quattro then look at getting the 6 speed gearbox from a leon, golf or bora.
along with the engine youll also need the ECU and instrument clocks - both these and the keys work together for the immobiliser .
youll need to get the keys programmed to the new ECU - need to find someone with VCDS and VAG commander to do this unless you find a nice dealer. otherwise youll need to get the immobiliser disabled.
Exhaus will need changed unless you can get a s3 version otherwise your going to have to get a 1.8t exhaust cut the downpipe and fit the flange for the biger turbo to it
the 1.6 has very small brakes as standard - ie the front discs are the same size as the rears on the S3. to get around this youll need the hubs callipers and carriers from the 1.8t minimum A3 should be 312mm discs fitted. get new discs and pads as youve no idea what condition the old ones will be in.
Cant remember is the actual suspension has to be changed as theres not much change in weight.
once youve done all that you can see how much its cost you then look to see how much a s3 2nd hand would be and itll probably work out cheaper to buy a new car then getting the parts swapping them, coding the ECU and then declaring everything to the insurance