When trying to improve your poor credit score, you need to look at the causes of the poor score. In your case, my guess is that your poor credit score is caused by two primary factors:
If you have late payments in the past, this is fixed by waiting and ensuring that you have no more late payments in the future.
But the number one thing you can do to improve your credit is to pay off your debt. All of it.
You are currently $14,000 in debt, and you are trying to add more debt to your life. That is the wrong direction to go. I recommend that you work to get completely debt free, (which will improve your credit) and then think about buying the house.
If you are planning on paying off all debt and aren’t going to take on new debt until everything is paid off, then it really doesn’t matter which order the debts are paid. Your score will be the same in the end no matter which route you take to get there.
Having said that, your smallest debts (and likely highest interest rates) are your three credit cards. Stop using those cards, and knock those out first as fast as you possibly can. Once you do that, you’ll have an additional $85 a month to put toward your bigger loans. Pay off the car last, as it is your biggest loan (and probably lowest interest rate).
You are paying over $1000 a month on payments for your debt, and a good chunk of that is interest. Won’t it be amazing when you have that debt paid off and $1000 per month more in your pocket? That is the goal you need to keep in mind as you work on this. It absolutely is worth it. Get there as fast as you possibly can. You can find ways to cut your expenses and get there faster. For example, you may want to drop cable TV or martial arts temporarily until you get out of debt; either of these moves would get you out of debt even faster.
Financing a washer/dryer from a rent-a-center is probably one of the most expensive/worst ways to purchase these items. Instead, look at buying a used machine from someone on Craigslist, or visit a laundromat until you have enough money to pay for what you want in full.
If you want more motivation on the benefits of getting out of debt and help on how to get there, I recommend the book The Total Money Makeover by Dave Ramsey.