Travel around and from South Korea (Seoul)

I heard the public transport is very decent in Seoul, but how easy is it to get around the country and does it cost much?

Is it worthwhile getting a car and if so, is it an expensive proposition? What are fuel prices, road tax and insurance like? Is it more hassle than it's worth?

What about travel from Seoul to SE Asia? Are there many budget airlines going travelling out of SK?

Many thanks for any advice.