Needleturn can be done either by hand or machine. It just means that the fabric is turned under around the edges. Raw edge can also be done either by hand or machine. Raw edge means there is no fabric turned under; the edge is simply cut.
Probably what you are wanting to do is fusible applique with a raw edge. This is the easiest. The edges do fray a bit with washings, but that is an expected look for raw edge fusible applique. You can do the stitching along the edges by hand or machine. Hand sewing through a fusible can be difficult, so most fusible applique is done by machine.
If you want the stitch to look like the one in the photo, you will need to do some experimenting with your machine. When I did this type of stitch on my Bernina 1230, I used a reverse blanket stitch and threaded my machine with 2 spools of black thread (treating both threads as if they were one when I was threading the machine). Doubling the thread made the stitch show up better. If you post the brand and model of your machine, someone here may be able to give you hints that apply to your machine.
If the picture will not be washed, you could even skip stitching and just mark the stitches with black permanent marker! If you do this, you could then machine straight stitch (quilt) around the outlines to achieve dimensionality.
You mentioned buying interfacing. Interfacing usually has just one side that is fusible. You can use interfacing with the Eleanor Burns method of applique (sew right side of fabric to interfacing, then slit the interfacing and turn the piece so the fabric has a lining made of interfacing), but most fusible applique using double-sided fusibles.
So you are making a pillow?