Any suggestions for a step up lens for a D3200 Nikon camera?

I'm a beginner photographer whose self taught and so far only have 18-55 lens that originaly came with the camera. I really like how the aperture can make the backround blurry and put the subject in sharp focus. Any suggestions? Open to anything.

Here are the factors that are included when shooting shallow depth of field images

* the length of the lens. The longer the lens, the shallower the depth of field
* that maximum aperture of the lens. When the lens is wide open, you will have shallower depth of field
* how close the subject is to the lens. When you have the subject at the lenses closest focus, the depth of field will be shallower.
* by placing the background further away from the subjects (like thirty or fifty feet sometimes)

With at least three of those conditions being met, you will be able to control the depth of field to your liking.

It really depends on what you like doing! For landscape and architecture then you'd be looking at a wide angle lens, but for portraiture you might be looking at a 50mm prime, while for nature photography it'd be a telephoto lens.

Quality counts, and so does aperture. Regards aperture, if you can try to go for lenses with constant f/2.8 or greater apertures!

I recently upgraded my camera body and lens from a D3100 to a D7200 and the 18-140mm stock lens that comes with it.

While it is undoubtedly a kit lens, it is a decent upgrade over the 18-55mm that comes with Nikon's lower cameras. And it is a good and cheap all-rounder lens.

50mm 1.8g, or 55-200mm VR…

55-200 VR is a good next step.

That's not a bad lens; in fact, I find that short zooms out-perform the longer zooms in terms of sharpness at both extremes, with far less distortions and aberrations. During the film era, I bought a generic zoom lens, and I sold it the day after I first used it; I found that most of the images had vignettnig; I got the Nikkor lens and have never had a problem with it; now, I stick with brand name lenses (Nikon/Nikkor). But that's my personal feelings about that; others here may tell you they've had more success than I had but the bias from the initial experience has stuck with me since.

My personal advice is that you try to get the best possible lens. And there are many reasons for that. First, it will affect the quality of images you get. Secondly, it's an investment for the future; you will have those lenses far longer than you'll have the camera body, and you'll be able to use the lenses on future camera upgrades. What kind of lens you may want to get next will depend on what you enjoy doing. Portraits? Landscape? Wildlife? Also, what is the budget? Give us an idea so we can try to help or guide you.

Enjoy that camera, and have fun!

Any lens that has an aperture of f/2.8 or larger such as f/1.8.
A 50mm f/1.8 or f/1.4 will be very inexpensive way of achieving the look that you want. The 50 f/1.8 is only about $125, while the f/1.4 is about $450.
If 50mm is not strong enough, then go with a telephoto like the 85 f/1.8, or a zoom like the 70-200 f/2.8. If the 50mm is too strong, then go with a lens like the Sigma 18-35 f/1.8.
The blurry backgrounds will be caused by your lens' aperture and it's focal length. That's why using short lenses like a 28mm at f/2 will still have the backgrounds with recognizable features, but the same shot taken with the 50 at f/2 will have blurrier backgrounds. The distance to your subjects affects the DOF too. Closer = blurrier background.

50mm f/1.4 plus a few good "BASIC PHOTOGRAPHY" books.

Good equipment is totally useless without strong supported knowledge.