need help deciding my cpu needs

The i3 6100 has 2 cores with 4 threads due to hyperthreading. It has a rated TDP of 51w, and generally matches or beats the FX-83xx CPUs in gaming, because most games rely heavily on 1-2 threads and can lightly utilize a few more. Each core on the i3 is close to twice as fast as the cores on an FX CPU. Although an FX-8350 has more total throughput, the i3 is faster in most desktop use cases by virtue of having much faster cores. This is generally considered the cheapest gaming CPU that won't have serious compromises.

The i5 6500 is a 4-core CPU without hyperthreading. Single-core performance is about the same as the i3, but it pulls ahead in multithreaded tasks, even beating the 8-core FX-8350. TDP is 65w. This is usually considered the best value gaming CPU, as it generally keeps even very CPU-hungry AAA titles like GTA V and Battlefield about 60fps, where an i3 might show some dips.

Both of these CPUs are 6th generation Core designs built on Intel's power-sipping 14nm process introduced in 2015 and fits into Intel's socket 1151, which is new and will be receiving at least 2 more generations of CPUs, and has modern features like USB 3.1, M.2, and PCIe 3.0, to name a few.

The FX-8350 is an 8-core CPU. The FX is build on Gobal Foundries' much older 32nm process (introduced in 2010), and has really high power consumption, generally exceeding 125w under load, despite being out-performed by the 65w i5 in basically everything. Its per-core performance was low even in 2012-terms, when it was generally outperformed in nearly every real-world task by the 2nd generation Intel i5 CPUs. It runs on the ancient and basically discontinued AM3+ platform which will receive no more CPUs, and hasn't received a new design since 2012.

Although it may sound like I'm disparaging the FX CPU, these are the facts. They're not poor performers, but neither are they faster than the cheaper and less power hungry i3's in most things people do. They still do alright in modern tasks, and can even make sense as an upgrade for someone with a much older AM3 CPU and a motherboard that can take the FX. The only time I would recommend building an FX-based system from scratch today is for a VM box, because VMs don't like sharing cores, even if those cores are twice as fast.