Component upgrade questions for my PC

[Boosted7M]

I currently am running a Thermaltake h22 chassis, MSI z170a-pro Mobo, G4400 (I only paid $40), EVGA 500w 80+ PSU, and an EVGA GTX 950 SC GPU. I currently use this computer as an HTPC/Console killer, but around black Friday I would like to do my first couple upgrades. This upgrade would be the CPU and CPU cooler.

My first question is about my CPU cooler. My case only supports a cooler 155mm tall and I have narrowed it down to two the CYRORIG H7 or the Phanteks PH-TC14S. What are the community's opinions on benefits or drawbacks for either cooler.(is one easier to install than the other, does one give better cooling, etc.?)

Second question has to do with my actual CPU, I bought the G4400 because it put me onto the platform that I wanted for the budget that I had at the time. I exclusively play at 1080p (Maybe 4k when TVs get down into the $500 range), but want to build so that maybe I can do VR in the future when that tech gets cheap too. So should I spring for a 6600k to take advantage of my motherboard, or should I consider other processors like a lower i5 or an i3 6100/6300?

Thank you in advance for anyone who replies. I do intend to get a better GPU, but that will probably be black Friday 2017.

 

[IDProG]

What is your budget for the upgrade?

 

[Boosted7M]

I would like to spend less than $50 on the cooler, and hopefully as far under $200 as I can for the CPU

 

[IDProG]

For $200, i5 6500 is perfect for your upgrade. It comes with a stock cooler, so you don't need to buy another one.
OR if you combine the budget, you can buy a i5-6600K and use the stock cooler from your G4400 so you can save some more money to buy a good CPU Cooler. Remember, you need to apply another thermal paste to be able to install the cooler.

 

[Boosted7M]

Thank you IDProG, When discussing the 6600 what type of cooler would you suggest. I know most people would say liquid or bust, but I am of the few people that prefer traditional cooling (I'm a very set it and forget it kind of person) due to its lack of maintenance. Are there better low profile air coolers than the two I mentioned above? If so what models and what are the benefits?

I bring this up because if I were to get a 6600k I would be overclocking it to a safe level maybe a little over 4ghz