There are four tire contact patches that are approximately the same size as four hand prints that keep your Bimmer stuck to the tarmac. You drive a Bimmer I'm guessing because you like a spirited drive every now and again, and perhaps more on the "now" than on the "again.".
Don't throw the dice on unknown and cheap tires. If you've ever read EVO Magazine or Car and Driver who do equipment tested tire tests, the "second tier" brands always do poorly. Michelin, Continental, and others consistently do well. There will be a time when you will have an "oh sh1t" moment and if you have cheap tires on your sled, you're going to throw a 7 and crap out, to use a gambling metaphor, but if you play the smart choice, meaning buying good tires, you'll throw the point every time, and who wins - definitely you.
Lastly, I'd say most people who buy premium car at full price have some scratch, and it's generally known you are going to open your wallet wide when it comes to maintaining your sled, especially one that has the blue and white fan on it. So the reality of the matter is, make the smart play and don't experiment with unknown or cheap tires.