The i5-8400 is cheaper than the i7s and almost as fast for gaming, where the bottleneck is almost always the graphics card. Dropping down to an i5 would let her fit a GTX 1070Ti or even a 1080 into the same budget - and that would result in a stronger gaming machine overall.https://techreport.com/review/34211/our ... -late-2018
If you're not going to buy a K-series i5/i7 CPU, you don't need the Z370 motherboard - an H370 board would be just as good and cheaper. The only thing a Z-series chip lets you do is overclock a K-series CPU. Again, the difference should be put towards improving the graphics card, as that is what makes the most difference to gaming performance.
I'm also an advocate for moderate air cooling of CPUs. There's extra risk and more things to go wrong with an AIO water cooler, and they're definitely noisier than an air cooler when the CPU isn't overclocked. I've had to repair PCs damaged by failing water coolers and it's not nice. The CPU either gets cooked due to pump failure or the waterbock being clogged, otherwise (pretty rare) there's a leak and multiple components are damaged at once. At least with a heatsink and fan, the cooling is often still within safe levels even if the fan dies, just because it still acts as a large passive cooler taking advantage of the case airflow. The Hyper 212 EVO is an amazing cooler for the money and performance is overkill for a non-K processor.
At 4TB capacity, my favourite storage drive is the Seagate Ironwolf 4TB. It's fast enough but one of the coolest and quietest disks on the market. As with most hard drives, don't assume that a different capacity is going to behave the same way - the Ironwolf 6TB spins faster and has more platters so it's hot and noisy. I've personally had bad luck and newegg reviews seem to echo my gut feeling that WD are not making quiet, good, reliable drives at the 4TB mark, though the Black models are warrantied for longer than the Greens or Reds, so perhaps their quality control is better.
If the budget isn't a big concern, I'd second (third?) the recommendation for the 8700K with a Z-series motherboard, and I think the 1070Ti is the sweet spot for gaming cards right now.