The 15"s look better/more correct but you won't find high performance tires for them. There are plenty of tires that are okay on the street and for open track events that don't involve sustained high speeds. And, "Yes", they will give a softer ride.
The 17"s are the only way to go if you want a high performance street tire and if you are going to do serious track work as the choices in high performance tires for street and track are much greater in the 17" size.
You just have to decide how hard you are going to push the car on the street and/or track. For a lot of folks the 15's are just fine.
If you can do it the best of both worlds is a set of 15" for the street and a set of 17" for the track.
all just imho of course.
