In general, for After Effects performance, the most important thing is clock speed of the processor. In some future versions of AE, the number of cores will matter a bit more than they currently do (the AE team has been talking publicly about how they're developing a more multithreaded renderer).
Also important is RAM. MINIMUM system required RAM is 16GB, but the suggested minimum is 32.
GPU is a bit important too as a number of effects render entirely on the GPU (the VR effects and a number of third-party plugins) or can be accelerated by a GPU (Fractal Noise and dozens of others), but this doesn't have to be crazy - just something decent like the 1000 series from NVIDIA.
Having SSD instead of HDD (and multiple ones, if possible, so your cache can be seperate) is also helpful.
So, knowing that, it should help you know for yourself what you can improve or not.
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