If you want your PC to perform numerical simulations, the processor is clearly the first component you should paid attention to. For this kind of application, Intel i7 and Intel Xeon are often used in desktop PC, no advertising intended.
Of course the frequency of the processor is important but look carefully at the specifications of the L1/L2/L3 caches, especially the size of the cache. A large cache is interesting (and expensive). That is an important information since the cache is a very low latency memory access widely used by the processor that can be used for specific optimizations (called cache optimizations). You should go to specific websites for detailed information, mainly Intel or AMD website's, especially for the ability of the processor to perform specific floating-point arithmetic operations, vectorization, hardware acceleration etc... It is very difficult to say that a processor is faster than another. However, you can have an idea of the overall performance of a CPU by looking at benchmark tests here
For running in parallel, the important is the number of cores. The core is really the component that perform the calculation. For a desktop PC, you could have 1 processor with 8 cores or 2 processors with 4 cores each, I can't explain you the difference. You should also paid attention to the ability of the hyper-threading which can in certain circumstances virtually doubles the number of cores. Remember however that running a code on 16 cores is not always faster than running on 8 cores, it strongly depends on the scalability of your code and the quality of your parallelization.
About the RAM, it strongly depends on how much data your code needs to store. Besides, don't forget that you should be able to post-process your data and visualization software often require huge amount of RAM. 16Go is a good start for scientific applications but that is very subjective. You may need a decent graphic cards for real-time or high quality rendering.
Of course around all of this, a decent motherboard with high-speed transfer and a (big) "fast read/write" hard-drive are required.