I had new carpet installed and I had them cut it so I can turn and tack the carpet over the edge of my new luxury vinyl plank. Now I'm looking for tips on how to get a nice straight carpet edge and what fastener (carpet tack. special stape, etc. I should use for tacking. I absolutely do not want to us one of those nasty metal edges.
To turn and finish a carpet edge, you use a carpet "z bar" along with tack strip. It will be nice and straight if you lay the bar and tack strip straight and are careful when trimming and tucking the carpet.
After tacking, you tamp down the z bar to secure the carpet edge. There are other designs besides the one shown in this image. Choose a heavy commercial grade bar. If your intention is to run this up and over the wood plank you will have a hump, most installers would finish it to the edge. My preference is to use a wood transition bar instead of the "nasty metal" type you describe.