The following wheel parameters will affect the handling of any car:
Offset
Size
Weight
Circumferential Weight distribution (ie is more of the weight closer to the point of rotation or closer to the outer rim)
Width
Roundness (some wheels are made to better tolerances and are 'rounder' to start with)
Material (related to weight but also more importantly strenth)
Generally with lighter, smaller and stronger the wheels, you get quicker response through the steering and suspension
Skinny wheels allow for skinny tyres which improve grip in damp / greasy conditions
Wide wheels allow wide tyres which allows the car to run softer compounds with lower sidewalls = more grip
Offset is hard to define as every car and driver are different.
Wheel width is related to the tyre width you shopuld fit (there are mins and maxs). Its bad to fit a wide tyre to a thin wheel and vice versa as the understeer / oversteer characteristics change on the car when this is done. However this can be used to 'balance' a car if you know what your doing.
Wheel width is related to camber and other supension parameters and so you should first decide what your goal is, then sort buy a wheel that works with your suspension to provide the desired result.
Simply buying a small, light wheel to 'imrpove handing' makes about as much sense as buying a house made of ice in Florida.