What is the best way for parent to give money from a house sale to a child - sell the house to the child then the child sells it or add the child's name to the house?

My father passed away 3 years ago. He left a house to my mom in Florida. She is from and lives in Canada. The house was bought for $560000, will likely sell for $470000. Mortgage owed is $240000. My mom wants to give me the money after paying the mortgage. Am I best to have her sell us the house for $1 and then I sell it. Should she put it in my name too then we sell it together? Or should she sell it and give me the money? What is the best tax strategy? Currently the house is being rented. He owned it for a decade. He put about $20000 into up keep.

thanks