What can I do to put the house and my dad's other property in my name if he died without a will? How much would it cost?

If he died without a will, then all his property would have to naturally proceed through intestate succession, handled by probate court. It becomes fairly complicated depending on his marriage status and how many children he had, but probate is meant to parse out the details.

What you have to do is start a probate estate asking to be named the personal representative. Then you have to gather the assets, notify his creditors, pay the creditors from the proceeds of the estate, then distribute the property to his heirs. Are you the only child? Was he married?