No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I would at least join a CU - the installment loan (credit builder loan) would be replaced by the car loan in this case - however, the point of the credit builder loan is to build a relationship with a local credit union.
The one I joined - they told me they just needed three TLs on my CR to be reporting positively for 12 months before I can refinance.
I had to get a car 1 month out ok BK, I had aquired a secured $300. card and that is all I had. I was approved for 17k at 10.99%.
Its possible. Good Luck to you.
Oh, and no. It won't tank your plan. Look in my siggy.