what sort of computer you planning to run it on?
Your app would be a very easy one to make. And also for performance, when you have zoomed out you can also just make lower triangle counts on the spheres.
Also because the human eye wouldnt be able to make sense of 5000 sphere arranged in double helix with only four colors. When you are fully zoomed out, you can just make a dodgy preset double helix shape to indicate there is more data, but when the user zooms, read from the file. I honestly think for ease of creation and protability of your app, lwjgl is a good option as it wont take long to make. You could also make webdemos for people to run.
If you want a really visually stimulating version with high quality graphics, try looking into JavaMonkeyEngine. its made using lwjgl and might cut out alot of basics (Also worth looking at for performance examples). If your interested in learning the basics of openGL, then yeah lwjgl is the way to go.
as for making it in c++ i dont think its worth it. not like the application would require a beast of a computer to run. and its harder to show off
