It's pot luck unfortunately, although I did read that mini's of that age are more reliable than newer ones due to better engine.
I've just paid £1800 for a 2008 Mini with 95k miles, so I'm hoping it will last 2-3 years without any big bills, anything more is a bonus, but I will keep it for much longer if it keeps going. I do see a lot of older ones around so there's hope.
Fortunately DP is a 'car man' so will do things like replace brake pads and we have a good reliable honest garage we can use for anything he can't do, but there's always a risk of clutch, gearbox or engine problems that are expensive. Plus auto boxes tend to cost more if work needed.
Have you checked insurance and road tax costs, some are quite high for minis, especially insurance for a young driver.
Who is paying for the car? Non boring cars are a luxury for a young driver, so unless she's paying insurance and repair costs herself, I think you should have a say in the matter. Although you could suggest she gets herself on YouTube and Mini enthusiasts forums, and gets herself a Haynes manual, do she can do some work herself if needed.