Performance wise, Intel edge out AMD when it comes to gaming, but not significant enough to really matter unless you're in pro-league. AMD works better as an production workhorse. I myself am building a new AMD build for myself now.
Case in point:
https://www.youtube.com/watch?v=iyaqSAotL3w&t=483s
As for cooler, some good air cooler are able to perform as well as some AIOs for a fraction of its cost. Examples is Noctua NH-D15 and Cooler Master Hyper 212 Evo (currently using the CM cooler). I'm not well versed in AIOs as I'm using custom open loop for my new build.
As for graphics, brands like MSI, Gigabyte, EVGA, Palit, and Zotac just to name a few. Asus cost significantly higher than the other brands, but you'll need to google for the benchmarks. I got my EVGA GTX 1080 from Amazon US as it cost exactly the same as buying a GTX 1070 Ti here.
Case will depend if you going water or air cooling. There are performance factors involve when it comes to component cooling within the case, but there's also the aesthetics factor that is subjected to individual taste, so it's each his own. I personally am inclined towards Fractal Design, so you can consider Define R6 for water cooling, and Meshify for air cooling.