The first step you would want to take is getting pre-approved for the new home purchase. Items that go into determining if you could get pre-approved are: credit, credit scores, employment, income & monthly minimum required debt payments (together it calculates your debt to income ratio), sales price, anticipated down payment, and assets/reserves (such as savings, checking, 401k, IRA, etc.).
First we go over the credit. A 597 credit score isn't great but can definitely still qualify. Since your credit has been on time for at least 12 months then FHA financing could very likely be an option. FHA financing would not require the charge-offs or collections to be paid, but lenders sometimes have their own "overlay" guidelines that could require them.. so when you seek out your lender that would be one of the questions you'd want to ask upfront before credit is pulled. I also think that your credit card utilization is bringing your scores down quite a bit, pay off/down your credit cards and you should see a nice score improvement.
You didn't lay out your income but I assume you make some, so what is your employment situation and how much is your income?
What do you anticipate will be the minimum monthly payments on your credit cards (and any other debt, like a car loan, student loan, etc.) when you apply? Are you going to pay off the credit cards with the sale proceeds from your current home?
What sales price range are you looking to buy in? How much are you anticipating getting as the net sale proceeds from your current home? How much of a down payment are you planning on putting down?
Outside of the sales proceeds, do you have other assets/reserves? This could be key in getting you a streamlined approval. The more assets/reserves you have after you bring in the down payment & any closing costs you are responsible for, the stronger your overall file is to underwriting.
After you get pre-approved then your next step is to get your home sold and keep an eye out for what other potential home you'd like to buy. You can make an offer contingent upon you selling your home, usually called "first right of refusal" where the seller can still accept other offers, but then if they do, you would be given the chance to remove the contingency that you would need to sell your home first - or you can just back out of the purchase contract. Or if you already accepted an offer on your home that makes you a more attractive buyer because then the seller of the home you are looking to buy wouldn't have to wait around for you to accept an offer on your home.
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