If she sells the home to you, your basis will be the purchase price. If you sell it for more than the purchase price, you will pay capital gains taxes on the difference between the purchase price and the sales
price when you file for that tax year.
If she gives the property to you, and the gift does not put her over her $1 million lifetime gift limit, she will not owe any gift taxes. However, your basis in the property will be the lower of her basis or the fair market value at the time of the gift. Therefore, if she bought the house long ago and has a low basis, you are going to get nailed for a lot of capital gains when you sell. Of course, if you live there as your primary residence for at least two years, you can qualify for a $250,000 exemption on gains.
One option is for your mother to retain a life estate in the property while transferring the remainder to you. In such a scenario, you have a property interest
in the property, but do not get full title until your mother's death. This allows you to get a stepped up basis of the fair market value of the home. The disadvantage of this method is that you don't get full title until death and cannot usually sell the home until your mother's death.
If your plan is to sell the home immediately, you would be better to have your mother sell the home herself, take the $250,000 primary residence exclusion then give you the proceeds from the sale.