There are different styles of back squatting, it depends what you are training for – bodybuilding, powerlifting, weightlighting, performance improvement for sport. All styles are good, but you would spend most of your time training the way that suits your goal.
The main things that will vary are stance (how wide apart your feet are) and bar placement (high or low on your back), and this will drive everything else.
No matter what the back should be remain flat or slightly arched, and you should usually go as low as you can without rounding your back, aiming to get below parallel eventually.
Partials are good as well to overload the top portion of the lift, but most people do partials all the time and think they are doing proper squats… they are not.