While I have not lived in that area I have spent a lot of time driving round there as the company I worked for had a lot of offices in the area.
The problem for traffic is that the whole area is cut off by the sea in the South, the estuary at Southampton, and Portmouth harbour. You have also have the New Forest in the way which causes a lot of problems for traffic due to narrow roads.
So almost all the traffic finishes up driving from West to East or East to West (unless it comes down the M3 from the North).
So you have thousands and thousands of people driving along the same basic corridor, making it a traffic nightmare.
So think VERY VERY carefully where you want to live before buying anything. Also practice driving the route DURING rush hour before buying anywhere, to see how long it takes.
You may find a 10 miles or 20 miles journey takes FAR longer than you think in the rush hour, and you dont want to be stuck doing it every day.