I belive you'd be better off paying down the credit card balances first. The reason for this is those balances are really going to limit the amount you can get approved for. I didn't add them all up but it appears to be in the neighborhood of 10k in Credit card debt. Getting this lower will give your credit scores quite the boost (especially mortgage scores) and that will help the interest rate in which you can get. So I would tackle the cards that have the highest interest rates first and get those paid down so your overall utilization is at least below 30%. You didn't list your income so it's hard to say if you could get approved for the 200k you're looking for. Also, do you have other debts such as Auto loan or Student loan?
I would suggest you look online for a 'Mortgage affordability Calculator'. There are lots of them around. They would help you determine what you might be able to afford in terms of monthly payments and house price. Basically the lender would take all the payments listed on your credit report (for credit cards and auto loans) and add those up. That will then be your debt obligations. I don't know much about the Homebuyers Choice program, so I'm not sure if they have specific DTI (Debt to Income) ratios that are required. It's great you have no bad information on your credit report. It seems the high credit card balances is the only thing holding your scores down.
A house is typically the biggest expense one will have in their entire life. And, even small movements in interest become expensive over the course of a 30 year term. Therefore, in my opinion, you should absolutely, positively with NO EXCEPTIONS, pay down your cards before trying to get a mortgage.
Below is a quick table on your current balances and utilization. Your scores are getting crushed by some of those balances. There are scoring penalties when aither aggregate or individual card utilization surpass 28.9%. And these penalties increase when you surpass 48.9%, 68.9% and 88.9%. (Anything over 88.9% is considered Maxed and gets an even bigger penalty).
Ideally you want your aggregate utilization to be below 8.9% and no individual card above 28.9%. If you truly do not have any late payments, charge-offs,. or collections, I can easily see your score well above 760 if you do, which will get you the best rates.
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