I would have expected your car to handle well, so have you checked the shocks are in good condition? Are the rubber bushes in good condition? i.e. for the anti-roll bar, strut tops etc.
Are the tyres wearing evenly? If not, it could be wheel alignment (camber, caster, toe-in etc).
Any of these could have an impact on the handling of your car.
When you write that the car feels like it's going to slide, is that oversteer (backend breaking free) or understeer (ploughing forward when you try and turn)?
If your car is front wheel drive you can expect a greater tendency towards understeer, when compared to a rear wheel drive car that tends towards oversteer.
I drive an 1990 Audi 90 Quattro 20V, and it handles superbly.............and more importantly, it handles predictably!