How Many Months Rent Should I Save Up For Before Looking For A Place?

My mom and I get along well and are close but we definitely bump heads (Im a gemini and she's a taurus if that helps you see where I'm coming from) and I feel we'd get along a lot better if I got my own place. I'll be 20 next month and she's been encouraging me to as well, not putting me out but just preparing me. I just got a job and after seeing my first paycheck I definitely think I'll be able to do it. Of course, though I wanna be smart about it. I already save in general because it's just smarter, but I was thinming of opening another account just for saved up rent money and how much should I have set aside? Btw I don't plan in going back to school anytime soon. I work at a hospital and they pay for education and I think I may just get into a program and then go from there