Best lens for portrait photography?

I have got the new Nikon D3200, and soon I would be taking senior pictures and I really need a good lens for portraits.

I want my pictures to be similar to these ones http://www.autumnburke.com/wp02/colorado-portrait-photography-ppc-workshop-senior-portraits/

What would be the best affordable lens to achieve this?

105 mm is the "standard."

On your APS sized sensor the 50mm f1.8 would be good, you need the wide aperture to get the selective focus shot where the background is blurred, but the subject sharp. The 'nifty fifty' is the cheapest way to do it. The 80mm f1.8 would be ideal, but expensive.

Don't think that just using a good lens will get you shots like those, look at the lighting and the attention to background, they look simple, but in fact need practice. Some of them use a flash with soft-box or umbrella, you can tell from the shadows and the tell tale catch-light in the eyes, the 'natural' light ones are not as 'natural' as they look, they are very carefully lit which takes time to master.

These photos are taken with +100mm focal length due to the compression of the background. The best lenses for portrait are the 85mm f/1.4 and the 50mm f/1.4. They are not zoom lenses so you can't zoom in and out but they are much sharper and wider (give you sharp subject but out of focus background) aperture.

Usually for a full frame dSLR, it will be a 80 to 135 mm. So for yours, as others have suggested, would be 50 mm to 80 mm.

The sample link you have shown us were well taken, and it was suggested that good lighting (to illuminate the subjects) is a big part of it, too. So don't jump into doing it for business until you learn how to use your camera.

Here is one taken with 135 mm f 2 at f 2 (same as a 85 mm on yours)