BATF and the GCA '68 make special exception to inherited firearms because now they are yours. They were transferred to you in a private transfer via the will or probate. Since they are yours you may ship them to yourself across state lines without involving an FFL dealer at either end.
Please accept my condolences on the loss of your father. If he got you interested in firearms and left you his guns, he must have been quite a man and thought enough of you to make sure you got them. A suggestion also, there may be some of the guns that you don't want because they may not be special to you. If you get rid of any of them, please honor your father by only selling them to an individual to whom the firearm would mean something. It meant something to your dad, so it would only be right that the gun be given a good home to a proud new owner who will care for it as your father did. I hate when some kids are left a beautiful gun collection that may have taken the better part of the last century to acquire and could easily span three centuries of firearms making only to be sold off to a local pawn shop for quick cash. Those guns were important to your dad, each one had a special memory for him and although he may be gone, his guns remain and therefore his special memories reamain alive in each one.