As we have already seen, and despite words to the contrary by SK, I think it would take a true invasion of SK by NK to start a full-scale war. Otherwise, I think it would continue with trading jabs, even though the South said it will retaliate heavily the next time the North does something. It seems like the kid who gets picked on by the bully and promises that
next time he'll fight back, but it is always next time. I'll probably hold this opinion until reality proves otherwise.
In the case of a full-scale war, I imagine we would fully support the South. As for the economy, it will have the same result as all wars have. Resources will be expropriated from citizens to pay for a foreign war where those resources are consumed and do not contribute to economic growth. In the process, the government will grow in size, scope, debt, and aggressiveness towards its own people. While this may result in a positive blip in GDP, that statistic won't mean much since resources will still be directed away from things that increase our standard of living, like houses, cars, computers, clothing, food, healthcare, entertainment (guns

) and etc. to produce war supplies. As nice as it would be to get rid of the regime in NK, dropping bombs on Pyongyang will not result in more plentiful, better quality, and cheaper goods in the US, it will generally be the opposite.
That being said, I don't think SK needs our help if it plays out under certain circumstances. Those being that China doesn't come to the aid of NK, and that the leadership of SK allows its military to fight with the gloves off, no hearts & minds campaign. This is because SK is a first world country with a strong economy, advanced technology, and a modern military; they will also have the moral high ground if NK attacks first (as far as I am concerned they already have the high ground). Conversely, NK is one of the most backward places on earth, where fuel and food are hard to come by, and the army is largely several decades out of date. The only real advantage that NK has is the size of its army and its likely willingness to win at all costs (I assume they are less likely to hold back than any western country, and in this case SK qualifies as western). If China jumps in, or the South tries not to be too "mean" (i.e. tries not to win too much), then they are in big trouble.
Of course, I'd much rather not find out what a continued Korean war would be, and watch NK crumble from within and eventually be peacefully reunited with the South. It will be interesting to see what the new guy does when Dear Leader eventually dies. Kim's son is in his late 20's, I believe.
edit: according to wikipedia (
http://en.wikipedia.org/wiki/List_of_co ... _of_troops" onclick="window.open(this.href);return false;), it looks like NK has an overall troop advantage of roughly 800,000, the advantage is around 400k of active duty. I thought the difference would actually be more than that.