No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I think you have a great chance for financing because if its a "Mom and Pop" dealership a lot of those guys use in house financing. Expect for you're APR to be high, and just remember for every $1,0000 you use as a downpayment, it's on $20 off of the monthly payment in my experience.
Find a nice $4,000 car.
Have a mechanic inspect it.
Pay cash.
Continue on your journey of improving credit.
Finance the car you really want the next time at a great rate.
$.02
With $2\4000 in savings and a low credit score, unless you make a very high income, I think the G37 is more car you can reasonably afford. The interest rate on the G37 will be unfavorable to say the least. If you make a high income, I would ask why you only have $4000 savings.
Pay off your personal loan and collections, work on your credit. Get a cheaper car as suggested above.
I kinda agree with @randomguy1
If this is your first car? dont go big just yet.
Maybe use half your savings, and save the other half for repairs or emergency.
If perhaps you have high income, why waste it on interest?
Interest rate is going to be astronomical and not worth it for probably over priced vehicle.
Take a look at something very reliable, perhaps an early 2000's Toyota Corolla/Camry or Honda Civic/Accord