Don't buy a Z for the ladies, buy a Z for you to enjoy. Most women don't care what you drive. When I drove a beater women would talk to me more often than not. When I drive the Z, or any other car I consider to be really nice/fancy, women seem to be intimidated or may feel the guy driving it is trying to overcompensate for other things they may lack in. IMHO if a chick really likes you and you hit it off she wouldn't care if you drove a beater. She might wonder to yourself if you ever plan on upgrading or think you may be really conservative with your finances. I will say though, I enjoy the look on peoples faces when they find out I drive a Z.
I paid 25K for my 09 Nismo used, I think it was a fair deal, my impatience got the best of me, I probably could have found a better deal if I had waited, but when they first came out in Hawaii they wanted 44k for a new Nismo. I bought a new base instead 32K out the door cash, waste of time and money since I no longer own it. What I am trying to tell you is to shop around, have patience, and don't drop all 20K cash on a car whereas you could put that money elsewhere for better use i;e investing. Use that money to repair or build your credit. Get a secured credit card for 10K use no more than 18% of that at any given time and watch your credit score increase.
When applying for a auto loan apply to as many finance companies as possible but do it within a week as the inquiries will remain on your credit for 12 months. I learned a lot from creditboards.com it took me a year to go from a 515 credit score to a 780, but I did a lot of research and work, was able to finance my house and put a nice down payment. Either way you go about it good luck. The Z is like family, it will always be here, the ladies will come and go.
EDIT: don't know if you are financing or giving a a huge down payment but I agree with the others have posted find a credit union or local bank and finance through them instead. 10% for five years is will cost you about about 10K in interest give or take a thousand. If you do go that route try to overpay your monthly payment if possible to hit the principal and reduce the life of the loan as well as interest.