That pretty well nails it. Sort of middle ground, not over the top with an i7 and not scraping by with a pentium dual core. The i3 is less expensive and does well in quite a few games but also falls a bit short and struggles in a few too. What sort of budget did you have in mind? Did you plan to buy a prebuilt pc or purchase components and put one together yourself?
A gaming pc is one with a decent cpu and a graphics card better than you'd need for basic email/youtube or movie viewing. Something like a locked i5 (non k) such as the 4th gen 4460, 4590 or skylake 6th gen 6500. For the graphics card, something around the $150-200 range like an r9 270x, r9 380, gtx 960 or better. Those should give decent fps at med/high or higher graphics...