I have a 2013 S5 with the 19" 5-segment-spoke design 255/35 summer performance tires. I drive around 20000 miles per year.

Any recommendations for winter tires? Should I just get new tires like the Dunlop SP Winter Sport 3D and have only the tires replaced every season or should I get new rims too?

If the latter, should I get 18" instead or keep at 19"? If so, what rims can you recommend matching the ones I have that came with the car? Don't need anything fancy. Looking at tirerack.com I see so many choices I am completely lost.

Get new wheels and tires. Generally its better for a winter tire to be a little narrower than a summer tire, so the 245/40/18 should be a good spot to start.

I have used the nokian hakk r on my car and cant say enough good things. They were the creator of the first winter tire in 1937 and pretty much have it figured it out. I have used all the other manufactures and the traction is not comparable in the slightest, also got three long canadian winters of use out of them. Save yourself some hassle, you will not regret it.