Cheapest method of rendering

I’m attempting to render 16384+ elements to the screen at once. What is the cheapest way to render several things on the screen at once. My personal thought right now is rendering several particles, but the issue that I’m having with that is that I do not know how to directly map the positions that I need to the particle and not have the particle die out on me while I’m trying to view the particle. A bit of background on this, I’m a part of a research group who is modeling NBody problems and I have a set of data that I need to read in, in order to view the information. I currently have the data rendered properly in SDL and openGL using point sprites, but I’m looking for a more portable solution (android, ios).

Do they share the same material and mesh? If so, surely batching is the way to go? Remember these days pushing vertices isn’t really the problem but graphics device state changes.