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Home loans

You can buy a home with little down payment, it just means your monthly mortgage payments will be a little higher. Your credit score is within the highest range and will get you a lower rate, but just barely. I got a 4% interest rate on my house and my score was a couple points below 800, in the 790s at the time. Now it's 800 even.
You could get another card and make on time payments on it for the next few years. The number of cards you have doesn't matter, it's the total amount available to you that you are using. The less you are using of it, the better.
Good luck and talk to a good lender. They answer a lot of questions. I'm also 32 and I bought my home at the very end of 2017.