I don't think the driving is too windy but it is what I grew up with so I don't tend to notice it. There is a bit on the way to Queenstown called The Devils Staircase, that is quite windy and hilly. There are usually metal barriers on the the side if it has a steep drop off. But the best plan is just to stay on the road lol.

You can definitely drive a circuit around, cheapest to fly into Christchurch and go from there. I would personally cut Southland out of the tour, so go straight from Qtown/Wanaka/Te Anau over to Dunedin (via Milton). If you are feeling adventurous you can go via Alexandra and Ranfurly to come out at Palmerston, beautiful countryside but last time I was that way the road wasn't entirely tar sealed -although it may be now. Unless you like to look at sheep and cows, then Southland would be good.

Milford Sound is totally beautiful. IMO it is the prettiest place in the entire country. When you are driving down the road to get there and the rain is making all the rock face turn into waterfalls... amazing. It isn't that much further from Te Anau than Doubtful Sound and totally worth it.