A few us run the Yokohama S-Drives, good in most conditions, pretty reasonably prices, good grip and don't wear too quickly.
I also have the Pirelli P-Zero Nero's and they seem just as good but were more expensive.
Don't forget to give Tyre Power North Melbourne a call for a great price and service! I know it is a bit of a trek for you, but it would be worth it. They know their MINI's and Tyres!