Performance Tuning – Which computer would be the fastest for Mathematica Home Edition?

If you use compiled and vectorized code, you can use as many kernels as your system provides, because parallelism is implemented by MKL and low-level routines such as BLAS. You can only use two Mathematica kernels at a time, which is almost no limitation Parallel-framework (which uses several Mathematica kernels) is almost useless. So, for numerical calculations, get the fastest machine possible. Things are different for vast symbolic calculations.

If you are interested in neural network installations, you may prefer NVidea to AMD graphics because only CUDA cards, not OpenCL, are supported. Anyway, most of the algorithms of Mathematica are not optimized for GPUs. Thus, aside from the very localized application of neural networks, the particular choice of GPU does not matter.

Think of it as the only general advice I can give: having a lot of memory is always a good idea and does not hurt anyway. Apart from that, I doubt that it is a good idea to build your new machine according to your Mathematica Licence.