That upgrade kit isn’t really worth it. The i7‑3770 is just an older CPU that’s only a bit faster than your FX‑6300 in some things, and the old H81 board limits you a lot. You’d be swapping one old system for another old system with only small gains.

If you want a real upgrade for a similar price, look for something like: a used Ryzen 3rd or 5th gen build (Ryzen 5 1600 / 2600 / 3600) with a decent board and at least 16GB RAM or an Intel 8th/9th gen build (i5‑8400 / i5‑9400 / i7‑8700) with 16GB RAM

Those options will actually feel faster in games and everyday use than both your current setup and that i7‑3770 kit.

So don’t take the 3770 unless it’s basically free and you’re just doing it for fun — better to save toward a modern platform.