Do you have direct deposit with work? If you don't, I would suggest you do that.
First let me say GOOD FOR YOU for using your own, hard-earned money on your car. I paid for every cent of my first car and am currently paying for my second car, as well. Unfortunately my first car only lasted 3 years, but it's still running good, I just wanted a newer car now due to planning for my future and saving for a house... long story. ANYWAYS. I'm glad there are still people out there who pay for their own stuff.
So I'm 20 in less than 2 weeks, and I have discovered an AMAZING way to save money like crazy, if you have direct deposit. Though it's easier for me since I make more, but it could work for you, too. I decided to open a new checking account at a different bank because there was an incentive if I had 6 months of direct deposit of over $100 each month. But now it's turned into something bigger. Each paycheck I put in $100 (twice a month). And it's my "non-existent" bank account because I never activated the debit card and I never got checks. And when I figure out how much money I have, I always forget about it. I've had it for almost 4 months now, and because of my start balance and my incentive, I almost have $1,000! So it is now my savings for a down payment on my house.
So since your paychecks are smaller, and you only have (rounded even) $300 a month to save, I would say each paycheck, put $50-75 into a new account. You can either be boring and not do anything or spend money for a year and save crazily and put $75-100 each paycheck, or you could live a little while still saving good money and put $50-75 each paycheck. I would recommend $50 a paycheck, though you may not be able to reach your wanted end result.
If you can't get direct deposit at work, give $60 or so to your mom each paycheck and have her keep track of your money somewhere and she can return it to you once you get your car.
Good luck and congrats!!!!!!!!