Hi
@Sewgood I agree with the other advice on laying the appliqué on top and leaving the mesh under, it gives a nice smooth finish.
You don't say if you already know how to sew stretch or have ever sewn a leotard before. If not then the first step is to learn how to handle the fabrics doing tests with cheap lycra and elastics, and then learn how to make a simple leotard.
Once you are happy doing that I would do lots of test swatches of cutting and sewing appliqué, it takes a bit of practice to get it looking good. Also once you start layering stretch fabric it can reduce the overall stretch so it is good to test for that reason as well so that your finished leotard is not too small.
If you are not drafting your own pattern then maybe try something like Jalie patterns, they are good for blending sizes between them and they make a wide range of dance and gymnastics patterns.
To make the appliqué pieces I copy out my overall pattern piece onto paper, then I draw the various appliqué shapes onto them. I trace these off onto another sheet so that I have both the main pattern for the mesh patterns for the appliqués. I then either transfer these designs to the fabric using chalk paper and a tracing wheel or by putting on top and cutting. I draw my designs freehand, I don't use templates, its not hard once you get going.
I looked through youtube videos and books on sewing stretch, swimwear and lingerie to help me learn the sewing part. I have also done some short courses in stretch/swimwear. You could try searching pintrest or youtube for something like - making/sewing rhythmic gymnastics leotards/acro leotards - I bet you would find some interesting stuff there.
For lycra I find the best needles are the 75/11 stretch - not ballpoint, which skip stitches. The 75/11 stretch are designed to stop the elastine fibres from sticking to the needle and breaking, causing the skipped stitch. I also find that a walking foot is very helpful for getting an nice flat seam, failing that you can put tissue paper under and or above your work as you sew. Stretch fabrics behave very differently but are lovely to work with once you get used to them.
Sorry if I've just told you things you already know! Good luck and let us know how you get on.