for your budget you would be looking at an intel i7 4 core build. if you want amd you should wait for amd zen to come out, but that might be a few months away for the 4-6 core zen cpu's. amd zen should be much better performance and value, but we will have to wait for reviews with adobe software. there is also some risk with using amd cpu's with adobe software, as it appears all of the devs and QA people use intel cpu's, leading to amd cpu bugs, and that could easily happen again with amd zen... also, after effects is being rebuilt to make it fully 64bit/multi-threaded. currently it only uses 2-4 cores and the intel i7 4 cores are the fastest with after effects. once they finish modernizing after effects it should use more cores like premiere.
after effects and premiere should be ok with amd gpu's. there are a few plugins and programs out there that only use nvidia, its kinda rare but still a few, so you would need to check against compatibility with any other software you plan on using. nvidia cards have a reputation of working better/faster with adobe, but a few people have reported solid/fast performance with the new amd rx cards.
Thanks for the input.
Are sure about the amd rx cards? Some people tell me that they are not very compatible with After Effects since the software is integrated with CUDA cores and it does not fully use the stream processors of the AMD RX cards.
there is at least one function of AE that needs an older nvidia gpu to work, ray-tracing. the AE team is trying to replace ray-tracing with C4D... this is a premiere pro sub-forum so you would have to ask on the AE forums for more info on amd gpu compatibility or issues. if you want to focus on broad compatibility and flexibility then you may want to skip amd and go with nvidia.