No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
If it's one or the other then my inclination would be to pay off the current car as you had planned.
I would purchase something nice but inexpensive. Even if you are looking for a luxury car, you can find a reliable W211 Mercedes-Benz E-Class (MY2003-2009) for under $10k. The V8s are more reliable and in better condition. You can also find some Lexus models which are even more reliable. I think going for a new car payment when you are worried about existing debt payments is misguided.