I will only comment on "how to buy a car cheap" others can comment whether you should buy a car in your financial situation.
That car is an absolute NO GO. 2012 with structural damage for $12k? Cars come with 5 year warranties, take advantage of it -- buy a 4 years old car.
Cars also depreciate heavily in the first 3-4 years of life, after which the price flattens -- again, buy a 4 years old car
Next, avoid popular models (Civic, Corolla), these hold value too well. You want that underdog no one care about that is actually a decent car. These cars will not be the things of dreams and will come with compromises. Many american brands and "second tier" Japanese area good fit here (Focus, Cobalt, 1st gen Fusion, Mazda6, last 2 gens of Kia and Hyundai).
This is where you start asking what compromises you are willing to make. For example .. everyone wants high mileage car. But high mileage will cost you* on purchase price. If you are not driving far, a car with comprably low mileage for its class (E.g. Chevy HHR vs other compacts) made it unpopular, and thus its resale value is lower.
(* I must say that high mileage cars are actually a bit of a bargain at the moment, because gas is cheap and Americans have the memory span of a goldfish).
You also need more research. There are some absolute sleeper cars no one cares about. For example, the Pontiac Vibe is the Corolla Matrix (down to the stereo). It's a pontiac, so its absolute steal on the used car market, but it's a Corolla, so it's bulletproof. 200X Corollas are virtually indestructible, Scions have horrible resale values (for what is basically a Toyota). Another odd choice if mileage is not #1 priority are ex-cop Crown Victorias. Not the sexiest cars, but you can get them for cca $5k running strong.
And finally, If you need this to be a daily driver, NEVER BUY ANYTHING BUT A CLEAR TITLE!
Finally, Avoid certified used. buy from owner on craigslist. Get financing from your local credit union.
Save the following search: Cars and trucks by owner, Clear title, newer than 2008, fewer than 75k miles, less than $10,000. You will be surprised.