Stretching hip flexors and calves is definetely way to go! If you sit a lot in your job/school, I think you should stretch them daily. You don't need any routine, just get in the position and squeeze your butt.
Also, free squatting is different then squatting with bar on your back. Heavy weight will actually help get into proper position. My form is better when I do heavy low reps, which may be a problem for a beginner who's still learning.
Dan John suggests doing 3-4x8 with 1 min rest or similar to learn proper form. Short rest periods will make last set (or two) very hard, so just think "ass down, chest up" and let your body do the rest. Unfortunately, I can't seem to remember where he suggested that (could be GetUp or on Prime Time).