IMHO if you're going to toss out RS3 as not being streetable enough, NT-05 is in the same basic boat. If you're going to hit track events regularly, though, you'll eventually want to be on a tire at least at the RS3/NT-05 kind of level (or R888, NT-01, or starting hitting some kind of slicks). Then again in TX weather I'd drive the RS3 on the street, unless we were in the few weeks of the year where we hit sub-freezing overnight. They don't wear as fast as the treadlife would seem to indicate if you don't drive like a maniac on the road, and they're not horrible (but not ideal, either) in the wet.
The second half of this set of clips is all on RS3's in the wet on a track that's not got the best pavement quality to begin with, showing slip+recover moments:
https://www.youtube.com/watch?v=OjEETzk7Pes#t=61
Also, while I'll agree with chops that the Conti DW isn't even in the same class as other tires discussed... it's decent, at least in the ballpark of e.g. the old Michelin PS2 street tires from a decade ago, and it has an incredible tread life even on-track. When I reached a certain point in my driving I ended up over-driving those tires and not wanting them on the car, but it it took a while, and the experience of finding the limitations of that tire and driving around them for a while was instructive along the way. Upside is they're definitely a streetable tire, even in cold/wet weather, but not snow/ice (which would be the DWS model, but I've never tried it and it's probably not as good for track use).
You could get a second set of wheels just for track tires too, so you don't have to compromise most of the time.