Do I need to buy * rated tyres?

I’m totally lost on whether I should be looking for * rated bmw tyres or the non bmw ones?

I’ve got a x3 m40i with Pirelli’s on at the minute that are near the end of their life. At £360 a corner I wanted to look at other options and found some Michelins at Costco for considerably less but the same size guide, they’re just not * rated so unsure if I should get them or not.

Anyone able to help untangle this tyre mess for me!