I'm a bit old-fashioned, but I still think applique done by hand (no fusible) is the best. My method is pretty basic, cut out paper templates (printer paper works or any scrap cards etc.), cut out fabric adding about 1/4 inch for turning over. Pin fabric to template and iron over to get a guide for the turnover, remove paper and tack design to background, then with thread that matches your applique piece do tiny hidden stitches to secure to the background. Alternatively, use blanket stitch or satin stitch.
There have been many stunning appliques shown on this site using machine/fusible etc. It's just a matter of finding something that appeals to you personally. I did handwork before learning to piece by machine, so I naturally feel a bit more comfortable with my method.
Let us know how you get on....and look forward to seeing your first applique.