Some good tips above.
I respectfully disagree with theoak, though, as I think the best way to increase flexibility is to work on squat depth instead of box squatting with a wide stance. Box squats are great for posterior chain strength, and will make you a beast. However, I think in order to learn form as a brand new squatter, you should focus on depth with an arch, instead of wide stance parallel squats with an arch. In my opinion, many powerlifters lack flexibility (careful, I didn't say all of them! and besides, I'm a PLer too) because they focus exclusively, or nearly so, on parallel squats. It's the rule in their competitions, so that's naturally the focus. Throw box squats in, maybe. Just don't make that the primary focus until you can full squat with good form.
In addition to the advice above, start overhead squatting. Start light, like PVC or broomstick light. Dan John is right, this is a very good way to learn squat specific flexibility. I don't know about your shoulder flexibility, but this should work on that too. Look up his stuff.
Ok, stretching is good here. Stretch the hamstrings, glutes, and calves. Don't worry about the lower back as much. A lot of times it's not actually lower back stiffness causing the rounding, but a combination of low back weakness and really, really tight hamstrings/glutes. Stretching your calves can help you hit depth at the bottom without shifting too far forward.
Just my 2 cents. Good luck.