Purely subjective - I like the look of 1 series more than Z4. And for me personally, 1M would make a better car since I am just a touch smaller than King-Kong and 1 has more head room
I don't know what your track experience is but, I always advocate a stockish E30 318is, 325i/is or a 944. $2-3000 worth of mods on any of these cars and you have a very good track car. Add a cage and you have a very good race car.
Just upgrade brake pads on any of those if you're just learning, or brakes, tires, suspension, cage if you're experienced and you're good to go.
So, to answer your question, I wouldn't choose a 1M, Z4 or any car worth well over $50.000 for driving schools.
And the best DD is a minivan! There, I said it... I must be getting old.