Your i3 is great for Minecraft. Vanilla Minecraft is heavily single-threaded so the extra cores won't help unless you want to run large modpacks, in which case an i7 would be ideal. Base on my own testing, some mods have multithreaded workloads and benefit from the extra threads an i7 has.
If you're looking for more performance in vanilla (or lightly modded) Minecraft, your GPU is more likely the better choice to upgrade. What GPU do you have?
And guys, about the motherboard and socket - the i3-6100 is an LGA1151 chip, so it'll work in any LGA1151 board and any consumer-grade LGA1151 chip will work in his board*, including the i5 and i7 OP listed.
*Xeon E3 v5 CPUs use LGA1151, but for this generation Intel decided to restrict their usage to C232 chipset boards. You can, however, use any LGA1151 chip in a C232 board.