Im looking to buy a new car..... but...?

I have never bought a car before, but I have had 3 cars in my life. Currently I am 26 and really thinking hard about buying a used car for the first time. The main problem that is holding me back is that.... Im kind of scared to do it. I have a few what if's that is holding me back such as: 1)what if i cant afford a car note one month? 2) what if insurance is to high? I have a car now that my dad gave to me that still works fine, but it is falling apart in a way and its reaching 100,000 miles REAL SOON. Currently I am a substitute teacher making okay money. I am also a grad student. Each semester I get about $6,000 in grant money from the school to pay for my apartment, take care of my baby girl etc. Next time I get the $6,000, I want to pay my rent for a few months with $2,000 and use another $2,000 to put a down payment on a car, the rest I will save. I will also get another part time job on the side to keep gas in it and pay insurance. The price range I'm looking to buy is no more that 18,000. I dont want to car note to me more that $350. I have found a few cars I like. So my question is, am I worrying too much and everything will work out just fine or should I not buy a car and pray that my old car dont break down? Thanks for all answers.