Many of my customers have been '1st time quilters'. They bring their quilts with the same apprehensions & fears you talk of and they end up all 'oh wow, I can't wait to show all my friends'. (It's the favorite aspect of my job.)
I've seen wavy borders, fullness, etc.; longarm quilting can minimize a lot of imperfections. Most LA professionals care very much about making their customers happy and take extra time and care, treating customer quilts with even more love and tenderness than their very own quilts.
Oh and remember, we are our own worst critics! Usually others looking at your quilt aren't in 'inspection' mode; they are just looking at the overall product and love'n it!