For all around use, yes, a true quad core is the way to go. But but for a budget build you can't beat an i3 6100. The following quote is from member Karadjgne, which states the reasons far better than I could:
"The i3 uses Hyperthreading. This means each core processes 2 threads, so maximum thread count as per any game or app currently is 4 threads. This is the same count as any i5. Applying 2 threads per core isn't as good as a single thread, so a true quad is more powerful per se. The skylake i3 6100 has better single thread performance than any Haswell or Devils Canyon cpu, has higher stock xpeeds than any but the 4970k. It's igpu iris graphics are the equal or better than an AMD a8 APU, which has 1/2 of its die dedicated to being an igpu.
With its price point, there's exactly nothing bad that can be said about the i3 6100. It's a very good base for your everyday 1080p gaming build pushing a gtx980 or r9 390 at most, with its best balance being seen with a gtx960 or r9 380.
Typically, amd rules the under $600 budget builds, until now, there's nothing amd makes that'll compete with an i3 6100 for a gaming rig at this price."