My biggest mistake when I built my first PC (which was 4 PC's ago now, needless to say I learned from my many mistakes) was when I cheaped out on the motherboard and cpu cooler. I decided to get an i5 4th gen, locked, a GTX 760, 8gb of value ram (which was later upgraded), a decent 500w EVGA PSU, and some gigabyte low level 1150 mobo.
Well it went well for the first month. With the stock i5 cooler I was getting okay temps at idle and relatively concerning temps at load. The motherboard, thought I didn't know it at the time, was falling short of what I expected.
One day while I was playing a game (I forget which - probably skyrim, or a total war game), my PC just shut off entirely. I found later that the motherboard had been fried and therefore fried the CPU. My 760 died shortly thereafter (I assume it became fried, too, but over a longer period).
I replaced the i5 with the exact same model and kept the stock cooler. Around 6 months after that, I was playing a really demanding game. I wasn't keeping track of my temps (because I was a beginner at this whole thing - I mean the Xbox never overheated!) and the same thing happened, got a black screen. I feared it was the motherboard, which was worse because I upgraded to a nicer ASUS board. Turns out the CPU overheated because the cooling system was not on par.
Lesson learned, I started using a hyper 212 evo after that. Now on my fourth PC, I'm using an h110iGTX with an OC'd 8320. And yes, this time I didn't cheap out on the mobo or cooler