My personal plan sounds similar to yours but I'm still living with family, you will not be. So more than likely you might end up paying rent, some bills, phone, etc... Also, how good is your credit score? It's hard to get a house, at least that's what I want by the time I'm 26, with no credit history/low score.
Living with your family is a free roof over your head, which gives you time to save up and even build your credit score. My buddy moved out and he has a car payment plus insurance, he pays about $500 a month in between the two PLUS rent which is an extra $250. Thats 3/4 of his monthly income gone, just on living expense. He has NO credit card as well... Meaning his credit score is very, very, low if not non existent. He cannot get a loan for a nice car/house on his OWN by the time I will be 26, but I will be able to on MY own.
My credit score is 710 and I'm the same age as you, I drive a nice car because most banks take a liking to me. I plan on opening another bank account with a credit card when I'm 21. My credit score will be 850($50k/any amount of money loan status basically) by the time I'm 23. I also make almost twice as less as my buddy whom moved out does yet I'm more financially stable compared to him.
I highly recommend you learn about financial stability before going anywhere, unlike my friend who is basically in the toilet in terms of finances.