I'm currently on a decent Dell XPS but its not great and I've had photoshop issue and sometime Premeire and AE drag.
My company has offered to get me a fresh machine, or see if upgrading this one with memory and a better card might be the solution.
Here's my basic system info:
Procesor: Intel(R) Core(TM) i7-4790 CPU @ 3.60 GHz
Memory : 16 GB
System Type: 64-bit Operating System x64-based processor
Running Windows 8
Video Card: NVIDIA GeForce GTX 745
I'm answering this from a strictly AE viewpoint since this is the AE forum. For Premiere, C4D, etc. the answers may be a bit different.
GPU: GPU doesn't matter much for AE. Like, it does surprisingly little. See here: GPU (CUDA, OpenGL) features in After Effects (It does matter for Premiere though; check with those folks on their suggestions.) Also, some third-party effects are GPU-accelerated such as Red Giant Universe, Element 3d, ShapeShifter, etc.
CPU: In AE's current state (and its history leading up to now), the clock speed of your processor matters most as long as you have enough RAM. From versions with multiprocessing (I think CS4 through CC 2014), having multiple cores would also help (for some comps) during render and for previews with multiprocessing, but multiprocessing could often be disabled by the wrong expression or the wrong effect and it was a bit buggy. The AE team is in the middle of rewriting AE's core. A future version will make much better use out of multiple cores.
But we're not there yet.
RAM: Make sure you have 4GB of RAM per core of your processor and you should be good. Also, make sure you're leaving enough RAM for your system while you're running AE! In your case, adding more RAM and making sure to allocate 2-6 GB to "other processes" might help a bit.
Hard drive: Having an SSD that AE can use for its cache separate from where footage and renders go can help a bunch with newer versions of AE (CC+).