As Boyd says in his book on Chebyshev Methods: when in doubt use Chebyshev polynomials.

I use Chebyshev polynomials extensively in finance and have tried problems like MNIST with Chebyshev and they get close to CNNs in accuracy.

ApproxFun Julia package pretty cool for Chebyshev work:

https://juliaapproximation.github.io/ApproxFun.jl/latest/