You have a couple of options.
Invisible thread is an option -- but if you don't like using it... you can get the same effect by using matching colors of regular thread. The closer the match -- the more "invisible" it will be. You could do a small zigzag, a satin stitch, a buttonhole stitch or even a straight line sewing stitch right along the edges.
By using a matching "invisible" thread -- you will get a more "formal look".
If you like the country or "folk art" style -- use a contrasting color for buttonhole stitching. Get a more "stained glass" look, do a satin stitch in a black thread.
You might want to do a "sample" block -- not as intricate of a design... and try out a couple of different edging styles -- and see which you like best before tackling the entire quilt. You have too much invested to start something you don't like and once you start a style -- you'll probably not want to change it.
Have fun with it!