With an E87 VL / VFL, you should simply be aware that you are buying engines that may be susceptible to chain damage. No matter how often it is discussed that only people who have had negative experiences write here - the fact is: the parts are dangerous if you do not even have> 1000 euros for repairs. (Here we only speak of identifying errors beforehand and changing the chain, of course not of engine damage).
The chain problem affects not only the 1 Series, but also other BMW models.
Nevertheless, I would say that the motors are not that bad in principle. The damage often amounts to broken chain tensioners. The consequence is that the chain has too little tension and skips.
Aside from engine problems, the E87 also have other teething problems. Turbocharger and differential also like to cause problems.
If you wish, I can recommend the 118d VFL to you. The engine is called M47. It is a little older and little or hardly susceptible to chain damage.
Unfortunately, the 6 cylinders are also affected by this problem. But you feel less often.
Nevertheless, I agree with the previous speakers: with good care and maintenance, you have a good chance that nothing will happen to the chain. But for that you would have to know the entire history of the vehicle - impossible.