Well THAT was certainly a teaching moment! It's one thing to think you are Mario Andretti, it's a whole 'nother thing to actually drive like him. Glad you are OK and have learned an expensive lesson. Fortunately, this is what insurance is for. Unfortunately, your rates will now go sky high unless your Dad claims he was driving the car (we won't discuss the moral issues associated with that).
There is no way anyone on this forum can assess what damage has been done or project what needs to be replaced. Your picture shows what looks to be a bumper laying in the road. It sounds like the visible damage is to both wheels and I presume you were able to drive home? If the car was towed, then the damage is more severe. You don't give model year or mileage either. If work has not been done before and the car has 100K+, you may opt to replace an entire axel's components. Control arms run about $125 each and struts go about $125-$250, depending on brand. Most importantly is if any damage occurred to the suspension anchor points (bushing mounts) on the car. If those are bent or damaged, expect to pay a LOT more to fix the car. Suspension damage is one of those things where you may never be able to get the ride and handling back to new. Only an expert mechanic can tell you what you need.