If you are running only a single simulation at a time, you should look for a processor with the highest possible GHz rating (including the Max Turbo Frequency). There are many high end processors that are 3.8-4.2 GHz.
Advanced User: My next suggestion is to have an Intel fourth generation or later processor and compile EnergyPlus yourself, but add "-march=native" to the compile flags. This will allow EnergyPlus to take full advantage of the more advanced architecture of these newer processors and more specifically be able to use AVX and AVX 2.0 instruction sets, which doubles the vectorization pipeline on the processor. Then in a year or so when AVX-512 comes out, it will be another doubling of the pipeline. In theory these advanced instruction sets should help EnergyPlus and decrease runtime, but your mileage my vary.
Then like others have mentioned, have plenty of RAM and ideally a SSD hard drive. I will say that an SSD hard drive, even if sometimes a marginal speed improvement for EnergyPlus, is a HUGE win for usability in general. It is by far the biggest bang for your buck and most noticeable speed improvement in easily the past 10+ years.