First you need to define "handling."
Wider tires may give you more grip on braking, and also perhaps on corners, provided that you update the alignment specs to keep them flat on the road at the higher cornering loads they may potentially generate. Stiffer shocks will affect control on rough or undulating roads, but in steady-state cornering conditions they don't matter as much, although an unmatched set of shocks, front and rear, can have a drastic effect on transitional behavior as you enter or exit a corner. Steady state cornering depends on, besides the wheel width and tires, a carefully tuned balance of roll resistance and alignment specs between the front and rear suspensions. If you're going to experiment, first consult someone who knows from experience your model of car and will talk honestly about your needs: a good suspension for autocrosses may be really squirrelly on fast freeway exits. Then start with tires, alignment, and swaybars.