It all depends on who you ask because different people can tolerate different settings when it comes to minimums. Some people can play at 1280x720 x5 @ 30 FPS, whereas others won't play at anything lower than 1920x1080 x5 @ 60 FPS. The hardware required to hit those two examples are much different, and without knowing what your expectations are it's really hard to say.
If you want me to take a guess, then I'd say that a current-generation (or equivalent) top-tier Intel i5 with a GTX 960 (or equivalent) for a bare minimum these days, and that's probably pushing it. An i5 may not have enough overall power to handle five game clients, and a GTX 960 may be struggling to push out adequate framerates when it comes to Draenor (WoD) or The Broken Isles (Legion) content. All of those components together (CPU, motherboard, RAM, GPU) are going to run at least $600, and then we're assuming that your older PSU can handle the newer generation hardware (and that we're re-using the case).
An Intel i7 is going to be the CPU you want to aim for, and then probably a GTX 970 (or equivalent), especially with the increase in hardware requirements for Legion, but those two components together are more than $600. It's difficult to upgrade after skipping several generations for a minimal amount of money because few pieces carry over to the new build.
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