My father is getting ready to purchase a home. He would like to make sure that his house avoids going through probate. Should he list me (and/or my brother) on the deed of his home? Or, perhaps do it another way (as an inheritance). Our goal is to avoid paying the least amount of taxes as possible (e.g., capital gains). Thank you.
So again, you must seek the advice of a Trust and Estate Lawyer. These things have huge learning curves. When my bro wanted me to manage all his finances he thought it was best to put me as his POA. But we soon enough found out that with his Trust, and his real property, some of his accounts, and his SS automatic deposit going into the Trust it was crucial I be also made Trustee of his Trust. So these things are complicated. You are dealing with some money. I encourage you to get books on Trust and Estate, learn as much as you can, get a lawyer for this stuff. As they always say "it's complicated".
It is never a good idea to be place on a Deed to a parent's house. Otherwise, you would be responsible for Capital Gain Taxes when you sell the house, and the bases used for the Taxes will go all the way back to when your Dad had purchased the house. It is better to inherit the house, that way the Taxe bases will only go back to the date of inheritance.
Also, make sure the full address of Dad's new house is placed into the Power of Attorney for later down the road, in case Dad is unable to do the paperwork for selling. It just makes everything much easier.
They can help your father avoid unintended consequences with property or capital gains taxes, gift tax return (but almost certainly no tax), personal liability, creditors, and Medicaid look back.
You can start doing homework now by looking at web sites like https://www.elderlawanswers.com/is-it-better-to-use-joint-ownership-or-a-trust-to-pass-down-a-home-15966
I also recommend a book on avoiding probate from NOLO Press, often available from local libraries in print or electronic format.