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Browse credit cards from a variety of issuers to see if there's a better card for you.
The payment amount will be included into your DTI and you'll likely need to show proof of regular payment history. (3 or 4 payements depending upon which loan product/program for which you are applying)
Based on your scenario, you are a good candidate for either an FHA or VA loan and possibly a USDA loan depending on your household size. We disregard all medical bills now so no need to worry about those.