It's basically a personal choice thing at the end of the day, and lets face it, although I don't like autos in general, I'd much rather have an auto Supra that a manual pretty much anything else!
As for the LSD, what basically happens with a conventional diff is that if one wheel loses traction then it becomes easier to turn than the other and all the engine's power goes to that wheel rather than the one that still has grip. When you power out of a corner, the inside rear wheel has much less grip than the outside one because all the weight of the car is on the outside wheel and the inside one has very little weight on it. With a conventional diff that inside wheel will spin as you put the power on. An LSD limits the difference in speeds between the two wheels, so instead of the wheel with the least grip getting all the power, the wheel with grip also gets some. That means you can power out of corners much faster. It also means that should you break traction with the rears they will both go rather than just one.
If you do a donut in a car with a normal diff, the inside rear wheel will spin on its own and the car will turn in a circle. With a LSD both wheels will spin which will pitch the car round the front wheels like a pendulum.
It's a fair bit more complicated than that as there are several different types of LSD that work in different ways, but that's the basic idea.