Shallowthought

Make sure its sitting right in the Case. All the pegs used to mount it are used and that the motherboard isnt touching at any other spots on the case. ( sorry for the delayed response) ( this is a longshot anyways just trying to help get to a solution)

If you can find one of the ones with the dual Quad cores they still work pretty well... I have one with the 2.66ghz quad cores. Its practical speed in rendering etc is about on par with a fx8350... (cinebenched mine vs my old desktop) If the price is right and u don't mind being on a dead and mac os it still works great for now. I use mine because I find Final Cut Pro to be the most intuitive editing software and because it works well as a good NAS for all my media collecting. (I paid $157 for mine back in 2016 and it came with the 4870 32gb of ram and the OS was on an SSD) So keep the price down Just make sure the price is right and make sure you use the sleep features these things are power hogs while on.

If I were you I'd invest in a nice set of Headphones... Remember your in high school... This means in the near future your going to be in college where space will be at a premium as well as your ability to blast music without being that guy in your dorm... A nice set of cans and a Headphone AMP would be my recommended route. but if you don't wish to go that route the posts above are all good advice (minus Tube amp... I'm yet to hear of anyone buying a affordable tube amp worthwhile.)

https://www.amazon.com/Audio-Technica-AT-LP120BK-USB-Direct-Drive-Professional-USB/dp/B00GA9COMM/ref=sr_1_3?ie=UTF8&qid=1550465529&sr=8-3&keywords=audio+technica+atlp120 Many of the offerrings around the $ price point are valid... Just don't cheap out and aim much lower than them. If you can find a vintage one in good shape they work as well. The downside is who knows how long theyll run or if they are still within manufacturing specs... god forbid they break.

Hmmmm... long shot but what size power supply do you have? Usually not enough power on the line causes failure to boot or unexpected crashes. Is it crashing at a time that would be "graphically intensive" The 1060 requires 120W or more if I'm not mistaken the gtx 750 only used 50 watts (I know this isn't usually the cause of these kinds of issues but you've already exhausted my first guesses)

Is it just the games crashing or is it the whole PC locking up?

Is the Motherboard grounded properly? (Long shot guess... you already checked the obvious things)

When you go into the Nvidia control panel does it show that the pc is choosing to use the NVIDIA GPU?

Make sure your computer sees the new Video card. Sometimes they will default to the onboard intel video. (Right click desktop go to nvidia settings) see if the Nvidia video card is selected. Also Obligatory check drivers.

The Senn's are great. I know my 598s have a phenomenal sound stage although I'd be lying if I said their bass leaves a bit to be desired... ( Will post review on the 6xx when mine arrive next month) (my 598s served me well for the past 7 years time for an upgrade) That being said I'm partial to Sennheiser due to excellent customer support I've experienced in the past.

Massdrop 58x or sennheiser 598's (ive heard many attest to the 58x being superior but can't personally attest)

If you don't have a quality pair of cans or studio monitors stick to your onboard. I blew up my sound chip on my old motherboard and had to get a sound card for the remainder of the life of that PC. I noticed a considerable Improvement in how well it pushed my Headset ( Sennheiser 598) or my wifes game zeros which are very similar anyway... But both of these are higher impedance headphones that average. If your sitting on a set of cans with impedance of 50ohms or greater give a sound card a shot it may open them up but otherwise stick with your onboards and save your money.