We are moving with Mom too. What telephone services, emergency services, and alerts should she have for when she is left alone?

Can you give more information please? Thanks.

You do not indicate if your mom has any problems.
Does she have Dementia? if so she should not be left alone even for a short period of time.
If she is able to use a phone a Land Line is most helpful as many areas so not have enhanced services and might not be able to pinpoint the location of a Cell phone call if it is an emergency. And with a recent move your mom might not know right off her address.
the Alert buttons are wonderful IF they can be used. For a person with dementia there is no telling when they will not be able to push a button for help. And more important they may no realize they are in need of help.
A little more info in your profile might help

????

This is a caregiver forum where we all share questions, concerns and vent our frustrations.

Not sure where 'there' is and what sort of info you're looking for, but I do think you are in the wrong place!