Your project goals are too vaguely specified to give a definitive answer to your question.
In the mean time, get a Raspberry PI 3 Model B. It's the latest, greatest, fastest, biggest Pi so far. And still pretty cheap.
That will make your software development much more comfortable.
When you have everything working nicely you may find that a Pi Zero or whatever will run the same code more efficiently. Then it's time to demonstrate that with a Pi Zero or whatever. Or just point out that it is easily doable in your project write up.
Memory in C++ is a leaky abstraction .