Up to you. If you plan to enter your quilt in a quilt show, you need to go through the effort of sewing your ends in. If not, then tacking them down and trimming the edge is not a big issue. Most will stay down for the life of the quilt. Some won't.
By the way, when you wash and dry your quilt, all sort of imperfections disappear, so don't worry too hard about wonky lines and curves. You are allowed to be a beginner.