One thing worth considering is that I picked the above list based on the cheapest possible platform that is still decent today. If you wanted something you can drop a newer CPU into and had a bit more money to spare it might be worth considering a build using a Ryzen 7000 or 9000 series chip. The physical CPU socket on those motherboards is likely to be in use for another couple of generations, meaning they would be upgradeable maybe even in 5 years time with one of the latest chips if required.
If you went ahead with this build you would need to reinstall Windows which would also require you to format the SSD, might be the IT shop could do that for you. A Windows 11 Home license is around 100, but you can also run Windows without activating it for free, you'd still need to download it to a USB from MS.
Learn how to create installation media for installing or reinstalling Windows.
support.microsoft.com
The power supply and motherboard would have all the cables required with it. The case should have all the screws and parts needed in there too, and it comes with 2 fans.
Have a look on Youtube for comparisons between the Ryzen 2700x and the 5600(x). The 5600x is quite a bit faster but how much depends a lot on the game involved. The 3050 still isnt going to set the world on fire but at least it wont be held back by the older CPU anymore at lower settings and you'll be able to drop in a newer GPU at some point with that power supply.
View: https://www.youtube.com/watch?v=55b7fyFqhRQ