Desktop Hardware and Upgrade Questions

Desktop PC reference: HP Omen 870-224

Present upgrades:

Samsung - 860 EVO 1TB Internal SATA Solid State Drive

A-Tech 32GB (2x16GB) DDR4 2133MHz DIMM PC4-17000 2Rx8 Dual Rank 1.2V CL15 288-Pin Non-ECC UDIMM

Present components:

I began playing a new Call of Duty game recently, and I'm having trouble running it in the quality that I desire. I bought an HP Omen 870-224 from BestBuy right around 2 years ago. I have added a 1tb SSD to my rig, and replaced the stock 8gigs of RAM with 2x16gig sticks. I have noticed that when I launch the Call of Duty application, my memory runs around 50% utilization, graphics card (which is stock) around 60%, and processors are running at 100%. The current processor is the stock i5-7400, which runs at 3.00ghz and claims to run at 3.5ghz turbo boost, but in task manager it's only showing 3.29ghz speeds.

Supported upgrades for the current build are the: Intel Core i7-7700 (Kabylake) 3.6 GHz Quad Core,

and the Intel Core i3-7100 (Kabylake) 3.9 GHz Dual Core.

Which of these would be better for gaming purposes?

I am thinking about upgrading the processor to an i7-7700k, which I believe is reported 3.9ghz with a 4.5ghz turbo boost. With speed, threads, and cores factored in, is this upgrade (~$400) enough to make a difference in my gaming, and actually be worth it?

If I do decide to go this route, my current PSU is the stock PSU as well, which will have to be upgraded. The i5-7400 has a 65w requirement, and I believe the i7-7700K requires 91w. What are the minimum specs for a PSU that would run my rig without more issues? And what other upgrades (if any?) will be necessary to support these upgrades? New tower, cables, cooling system?

Thanks in advance.