Putting our out-of-state family home in my name, things to watch?

My mother is in her mid 80s, and our family home is completely paid off. She wants to put me on the deed as sole owner. I reside in Seattle, the home is in Albuquerque NM. I'm told the smoothest way to do this is to first put both our names on the deed by adding mine making us joint tenants, and then having her sign a quit claim deed.

The goal is to have the house in my name sooner than later while paying as little fees as possible. Is the above method the best method?

Also what is the process of the property taxes being transfered to me, as well as insurance or utilities, how do I calculate the tax increase from her old locked-in rate to a new one in my name, what does being an out of state resident do to this process, is there a benefit to me showing residency in New Mexico, is there anything else I am missing?

Lastly how will this affect her medicare? Are her premiums dictated by her net worth/asset value and will this transfer of ownership affect that in any way? How do I prevent any negative effects there?