Thank you Moss for both your general suggestion to buy an old machine and also for the detailed technical suggestions. 

Until a couple of years ago, I have always bought new computers (except early days when it was possible to get very old almost for free at my work). 

I have instead of using eBay equivalent bought my old refurbished computers online directly from companies (here in Sweden) focused on refurbished IT. They might be somewhat more expensive and the offerings more limited, but the advantages to buy from those selected companies with good reputation are that they grade the equipment plus gives warranty. When I have bought with the best grade, the computer (and phone) looks as it is brand new. 

So I indeed agree with you to consider to buy an old computer, as well as to consider Linux of choice.