I'm a tyre engineer by profession & love reading some of the things written about tyres…
Makes me smile
Personally I would be nervous about fitting part worn tyres just because there is so much within a tyre that you cannot see. It's a fair comment that if you buy a 2nd hand car that is what you get also but I would certainly have a thorough check of the external condition of the tyres fitted to such a car.
The Auto Express team make a pretty good tyre test (it used to be available online), as do many German car / consumer mags. How's your German? check out the website from ADAC (reifentest).
General advice is buy one of the major branded tyres if your budget stretches to it. Pirelli, Mich, Conti, Goodyear, Dunlop, Bridgestone, Firestone. Hankook & Kumho are now also quality products.
Certainly in my company our tyres are tested very thoroughly for all performances & frequently evaluated against the other premium bands.
Most important advice is to avoid the very cheapest import brands from asia. There are surprisingly big differences when it comes to life saving performances like wet braking. It may be even that the ABS calibration no longer matches the grip level of these tyres and the net effect is a huge increase is absolute stopping distance.