I've always used 4" screws...and use Grade 8 screws!3" screws at a minimum. Door Devil or other products could also help. But frankly from what Ive seen, the 3" screws are enough for all but the most determined. (e.g. SWAT battering rams)
At the minimum, the repeated banging (kicking) on the door is enough to alert you and give you a few extra seconds to react, grab the kids, get to a secure room, get on the phone with 9-1-1, access a weapon, etc. I've helped a few lady friends 'fortify' their apartment and/or home and have always used 4" Grade 8 screws.