There's nothing wrong with buying cars from family, as long as everything is done above board. Financing through a family member is another animal altogether and I advise you to avoid it like the plague. If you do so, every financial choice you make becomes your dad's business. If you stop by and are holding a $4 cup of coffee, he will wonder if that will affect your ability to pay him that month (it will be an involuntary thought and he would probably deny thinking so, but that thought will cross his mind). God forbid you miss a payment or even make it a bit late! Yes, he will "understand", but will not like it and will judge every financial decision that much more. Job loss? Emergency? Total that car?
What you will owe him will be more than just money and everyone will know it, even if it is not vocalised. It isn't worth it, even if he charges you no or little interest.
I warn against financing anything other than a house, but if you must finance it, do it with a local credit union, put down as much as you can (keeping $1,000 as an emergency fund), and then throw everything you get as a settlement from your or the other driver's insurance company at the loan to pay it off ASAP. Even if you get a higher interest rate because of not being able to put much down, you can refinance after paying it down.