LSD on a stage 1?
Not many have done that. Id say decent tyres and maybe the walk kit will sort it.
Who mapped your car? if its spinning early in the revs then sound like a lot of low end torque?
Not many have done it because it's expensive and they can't take it out to sell the car. Those that don't have one will tell you they're not necessary. Those that have them will tell you that they're worth every penny. And they are.
Anti-lift kits of one sort or another are very worthwhile. Engine mounts help but are not solely responsible. There is an awful lot of engine movement on these as standard as the whole car is set up to be very smooth and compliant. The engine behaves as a big pendulum and can assist in destabilizing the front end. No one thing can miraculously cure these issues but the sum of a number of changes can help a lot. It will always be a FWD and as such will need a degree of finesse in adverse conditions. Your goal is to stop geometry angles changing under differing loads and to 'button down' anything that has mass and can move around within it's mounts, such as the engine for example.
Imagine you're under hard acceleration and the engine is pushing back in it's mounts, you lose traction, the engine returns to a 'normal' position due to the load on the drive train reducing to nil suddenly, you regain traction, the engines pushes back in it's mounts and so it repeats.
Throttle control is improved massively with a good set of engine mounts. You can modulate the throttle properly instead of wasting some input in overcoming the cushioning effect of the OE mounts.
Reducing un-sprung weight can help. S3 calipers and discs for example are extremely heavy and all this weight is bouncing up and down on the end of a suspension leg.
Stickier tyres will also be a good thing to invest in. Michelin Pilot Super Sports are a good one to look at. They can manage track days as well if you ever needed to. I have them and have particularly enjoyed them in the wet. No issues at all.
You also need a degree of compliance in your suspension. Harder is not always best and can work against you. Some of the very best suspension set ups are far from the hardest.
No two people are bound to have the same opinion about the same parts since there are so many influences which can and will affect what you are trying to achieve. And then there's your budget.
