The Ryzen 5 3600 is superior to the 9700K for less money, so no, that CPU is no good as an option.
The first build with the RX 580 is no good either, that card is roughly equal to a GTX 1060 6GB.
The 3060 Ti is far newer, and far more powerful, offering you RT cores for ray tracing and DLSS 2.0 upscaling as well as other nice features built in that Nvidia has had on their cards for a long time now such as NVENC for dedicated hardware encoding (things like video editing and streaming)
The 5500 XT is newer for sure, but not the newest, and I wouldn't pick that over a 3060 Ti either.
(Pretty sure it's not even as powerful, and the 4GB of VRAM barely makes the cut these days for AAA titles, and isn't gonna cut it very well in the coming few years.)
Overall, those builds are horribly balanced in regards with price to performance ratio.
While the PC case you picked out is "cool and shiny" looking, it's not very good when it comes to airflow and thermal performance.
If you want a shinier looking case than the one I provided, (which has great air flow btw) and are willing to spend the extra money to get it, then here is an updated version of the build I provided earlier with a shinier case that comes with a fan in the rear and fans in the front.
You can add additional fans to the top of the case at additional cost if you like, or save that space for moving the front fans up there if you want to opt for a third party AiO cooler or something for the CPU.
A different cooler is not necessary for the 3600 if you don't plan on overclocking it to super high overclocks.
The cooler that is included with it can handle a mild overclock on it's own.
PCPartPicker Part List
CPU: AMD Ryzen 5 3600 3.6 GHz 6-Core Processor (£188.88 @ More Computers)
Motherboard: ASRock B550M Phantom Gaming 4 Micro ATX AM4 Motherboard (£87.23 @ CCL Computers)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory (£70.75 @ CCL Computers)
Storage: Intel 660p 512 GB M.2-2280 NVME Solid State Drive (£54.35 @ CCL Computers)
Video Card: MSI GeForce RTX 3060 Ti 8 GB VENTUS 3X OC Video Card (£469.98 @ Ebuyer)
Case: Lian Li Lancool II Mesh ATX Mid Tower Case (£97.07 @ Overclockers.co.uk)
Power Supply: Corsair TXM Gold 750 W 80+ Gold Certified Semi-modular ATX Power Supply (£96.47 @ Amazon UK)
Total: £1064.73
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2021-01-09 01:52 GMT+0000