Turning and tacking carpet where it meets vinyl flooring
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.