I currently have one of each generation in my house. My R53 was bought new in 2005. It currently has 264000 kms. A high mileage car. It is lightly modded. Over it's 15 year history, other than the normal routine maintenance, unexpected maintenance items include accessory belt tensioner (on it's 3rd one), Top engine mount (on it's 4th one), front windshields (on it's 7th one), fuel pump (was replaced under warranty), Power steering fan (replaced under dealer recall). Recently replaced an alternator, but at 260,000 kms, that is a very good lifespan. Driver side rear fender marker light melts when the bulb burns out so you can't just replace the bulb. Other than that, my particular car has been extremely reliable, though I maintain it fairly meticulously. I've seen other MINI R53 owners have a lot more trouble. Extemely fun to drive. Best overall car I have ever owned, for my purposes, in my lifetime of driving.
R56: Bought by my kid who paid for it herself because we have had good experience with my R53. Rear light fixture circuit board melts. It is not covered under warranty. Dealer we bought it from was kind enough to pick up 80% of the tab since they sold us the car with the fixture already having issues. Other than that, just oil changes and routine maintenance. Drives more like a BMW and less MINI like. If you go for an R56, you should consider the GP. The brakes themselves are worth the price of admission.
F60 Countryman Cooper S with All4. Very BMW like and not at all like a MINI. Best carlike handling small SUV of any I have driven, but still an SUV. Engine drones a bit when cruising. The bottom transmission mount under the car seems a bit fragile, as my wife has managed to break one. Since she bottomed it out on a parking curb, it was not covered under warranty. It's very expensive to replace. The sport seats are really really good.
As far as engines go. The super charged is the most fun to have. If you have a reduction pulley, the super charge whine above 3000 rpm is so intoxicating. The turbo engines, you don't really know there is a turbo there. The turbo has been integrated into the power band very seemlessly. It makes good power, and you get better fuel economy. From about 2010 on, they were pretty good. You should probably avoid the 2007 Turbo motors unless you know the recalls and updates have been taken care of.