You are almost there. All you need is a mobo and a psu. You have the 1050ti so may as well use it , can upgrade when you like.
Here are my suggestions for components with comments below.
My basket at OcUK:
Total: £536.65 (includes delivery: £11.70)
Choice of mobo. One mini ATX with wifi but you have full sized case so you can get the normal ATX if you prefer. Not sure if you will need wifi or not.
PSU choices became more complicated over past week or so with the release of the 4090/4080 and the new spec power supplies that are designed to go with them. Firstly , there are problems with old psus and these new cards , they do not communicate like the new psus will and therefore the gpus may pull more power than the psu can supply. Secondly , they have made a mess of the new connectors and they are way too fragile and I expect an updated spec within a year to address this problem.
Power supplies went from simple to problematic overnight and not been in a situation like this for over a decade, it is a mess.
This means if you want to buy a PSU that is suitable for you needs at this moment in time with a 12100f and 1050ti then the 550w or 650w above will do the job. If you want to buy a psu with a newer card in mind then its very hard to advise because the new spec psus are just being released and they have design flaws that may or may not affect a person, we just do not know.
Win10 will work fine with a 12100. The lower end Alderlake chips such as the 12100 and 12400 only have Performance cores and no Economy cores. This means you do not need the fancy thread scheduling in Win11 to make them work correctly and Win10 will be fine.
Win10 is a free download from the MS website. You can run it without a key , i am, or you can purchase/source a key yourself.