Okay - alloy wheels are generally lighter than steel wheels.
So - there is therefore less rotational inertia (ie. less weight) for the motor to overcome to start rotate the wheel - ie. better acceleration and engine response.
Unsprung weight refers to weight that isn't carried by the suspension of your car - ie. outboard suspension components, brakes, wheels and tyres. Since this weight isn't suspended, it's effectively uncontrolled (well, not totally uncontrolled, since a by-product of the suspension keeping your car's body off the road is that it pushes the wheels down.
If you minimise this unsprung weight, it means proportionately more of the vehicle's weight is suspended, and therefore can be controlled by the suspension, leading to better handling.
It's pretty marginal stuff, but there are benefits.
The issue with bigger wheels is mostly a road thing - once you go over about 16-17 inches in wheel size, you lose a lot of tyre wall flex (ie. the tyre wall bending as it hits a bump, cushioning bumps), and consequently, the wheel is more likely to bounce off bumps, so you don't get as consistent a tyre contact patch with the road, so you actually get less grip.
Similar thing happens with tyre width - it's possible to go too far in tyre width, especially with lighter cars. If you think of the size of the tyre contact patch in the context of the car's weight (so, wider tyre means less weight per square inch of contact patch), you can get to a point where grip is actually reduced, because there's too little weight for the width of the tyre.