[lukits01]

Usually normal commuter cars are setup to be understeery as to promote stability at high speed. E.g. swerving to avoid obstacle at freeway speed without losing control. Unfortunately this numbs down the handling at day to day cornering speed. Adding a rear swaybar will make a difference to the feel of the car on day to day cornering speed, but of course now you've moved away from that factory "safe" setup.

As to how big, it's all relative really, the rule of thumb at least on the track is for FWD cars, you just want the rear swaybar to be just big enough to be able to lift up the inside rear wheel when cornering and no more.