I live in GA....never been to Grovetown, but in my rural area it is completely reasonable to expect $20k in repairs with cheap entry-level finishes on most 1200 sf mid-60's brick ranch homes. I believe you when you say yours needs only $10k, because I've seen it before.
So, worst case, you need a little less than $40k. If you've got some cash saved up, you could easily get the rest from a place like Lending Club, Propser.com or even your local bank with a signature loan. Since you're employed, you should be good to go. Depending on your credit (you're so young, it hasn't had time to build yet), the rate may be horrible, but work that into your numbers and plan for it. Use the calculator on this website to really analyze your numbers.
But, honestly, it sounds like you've done all that so I would go secure your funding and go for it. If you fail, you are young enough to recover. You can't succeed unless you try and failure is how we learn things, so either way its win/win.
My only advice is that time is money. Get in there quick, get it fixed, and list it.