Paying your bills is simple arithmetic. XYZ coming in, ABC going out. Don't make it more complicated than it has to be. When you get paid each Friday, pay the bill that is due the soonest.
Also, I would suggest you find ways to cut your bills down some. The rent seems really high to me, but I don't know where you live. What's your lease situation? Can you get out of it and live with your parents? Or maybe find a "temporary" roommate. If you have 2 bedrooms, you should strongly consider finding a roommate. They will pay half your rent. You can find someone who just needs a place for a few months until your boyfriend comes home, or maybe on a more permanent basis. That will help you save a lot of money.
Also, the car payment seems high too. I drove a brand new car and only paid $270 a month. What kind of car is it?? Might be time to trade it in for a older/less fancy car. You don't need to drive a piece of crap, but something a bit more economical.
I pay $35 a month for a cell phone. It's one of those "pre pay" phone card types, but believe me it works the same as a fancy phone plan from ATT/Verizon/sprint/whatever but it's just a third of the price.
You didn't list any kind of groceries or anything. You mentioned not eating out, which is great. I will suggest looking into coupons. They are such a great way to save money on food, and let you "stock up" for times when maybe your check won't let you buy groceries. Also, a lot of grocery stores offer rewards/points at gas stations, so it would behoove you to shop at one grocery store and earn rewards on gas. You'll also be able to find coupons and deals on dog food, which will help you save there too.
You have the right mindset about the CC. pay them off, ASAP. However, that is hard to do when you don't have any extra money freed up to pay them. It should go without saying that you shouldn't use them. If you can't pay cash for it, you don't need it. Unless it's something that you would literally die without, don't buy it unless you can pay cash.
I hope some of this helps.