On crop sensors, 35mm is easier to use (than 50mm) because it is a normal focal length (approximately equal to the length of the diagonal of the frame), but 50mm will get you more blur because of the longer focal length when the camera-subject distance is kept the same.
If you're open to trying some sharp, manual-focus lenses, 35/2.8 and 50/1.8 lenses tend to produce reasonably good background blur at normal distances (about 180cm). Lenses with M42 mounts that can be adapted to Nikon bodies are pretty inexpensive, so you can get one of each focal length to try. Then when you have more experience, you can spend more on your dream lens.
Increased background blur is associated with the following:
- Larger apertures (smaller n for f/n).
- Longer focal lengths.
- Subjects much closer to camera than to background.
You are able to get good background blur for portraits with the kit lens because the aperture is large enough (f/5.6) for the focal length (55mm) when the subject is close to the camera. However, when the subject moves away from the camera, the aperture becomes inadequate. When you zoom out (18-24mm), the aperture doesn't get large enough (f/3.5) to compensate for the change in focal length.
Just getting lenses with larger apertures doesn't necessarily solve the problem. The focal length still has to be long enough, and the subject still has to be close enough. That is why compact cameras with tiny focal lengths don't get good background blur at normal subject distances despite having f/2 apertures. This issue with smaller focal lengths doesn't affect you too much now since you ask specifically about 30-50mm, but you should be aware of it for when you start looking at lenses shorter than 28mm.
There's also subject-background separation (or isolation), which is somewhat related to background blur. I'm not sure of all of the factors involved, but increased background blur is not necessary, nor sufficient, to produce good subject-background separation. For instance, I had an old Tokina-made 35/2.8 lens that produced surprisingly good subject-background separation at f/5.6, though it was a bit soft wide open. The bokeh characteristic of that particular lens was a medial highlight with a lateral smear. Bokeh "balls" looked like "popped" bubbles. This seemed to be able to emphasize the subject while de-emphasizing the background.