No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
When we applied for our mortgage, I had a charge-off from an auto reposession in 2011. For me to move forward in the process, our lender stated that I needed to have the account closed and report a $0 balance. I contacted that bank and ended up settling and not paying the full balance. In my case, the full balance was $1600, and the bank made me pay half of that. The reposession will be removed from my credit in January 2018.
You should check the statute of limitations in your state for auto charge-offs. If you're still within the limits then the bank that has that auto lien may not be willing to settle with you for a lower amount because they technically could still sue you for the full amount if they wanted. If you aren't in a rush to buy a home, I would wait until you are outside of the statute of limitations and try settling. You have another 4 years to go before it's removed from your report.