Tyres are obviously a very important part of the handling equation. If they're worn from the original profile, then they will degrade handling, whether it be due to bad feathering, squaring off due to many motorway miles or whatever. No amount of expense on suspension mods will really compensate for this, but good suspension and good tyres combined will always be the best way forward. Might I suggest Michelin Pilot Road 2s as a reasonably priced solution? An excellent tyre from the performance point of view, superseded now by the 3 and 4 of that series, they can be picked up for a good price, although again, might be worth checking shelf life now.