If I understand correctly, Abramski v. US, (*1), would indicate that your father cannot purchase it on your behalf and transfer or sell it to you. (This case was nephew/uncle, so family is NOT exempted). At issue is Form 4473 (*2) question 11a where he would be required to indicate that he is "the actual transferee/buyer of the firearm". If you give him money to purchase it, or agree to purchase it from him afterwards, he would be treated as your agent, and answering this question as "yes, he is the actual buyer" could be a felony straw purchase.
But it looks like him buying it for you as a gift is a good option. Following this same form, on page 4, clarifying question 11.a. "You are also the actual transferee/buyer if you are legitimately purchasing the firearm as a gift for a third party." It goes on to state explicitly that it must be purchased with the purchasers own money and then given as a present. So no gimmicks where he gifts it to you and you gift him the money, or things like that... they threw "legitimate" in there to ensure no games were played.
If you live in the same household, I don't see any reason he couldn't purchase it for himself but allow you to carry it whenever you like. I believe that CCW allows you to carry any firearm you legally can possess, not limited to ones you own, so any member of the household with a CCW should be able to carry it. If you live in a separate house, I'd worry about it being a gray area in the straw purchase as far as transferring to someone else (if he didn't "gift" it to you).
If he doesn't have the money to gift it to you... have him purchase it, then shoot it a bunch at a range for a couple months before selling it to you. Adjust both the time and usage to an amount that you would feel comfortable defending as him having purchased it for himself before reselling.