The one everyone should have is a smoke detector. At least one for
each level of the house, preferably wired together so they all will go
off if one alerts.

After that, CO is also very important, if you have sources in the
house that burn fuels and could generate CO, ie gas/oil furnace, gas
water heater, wood stove, etc. If all you have are elec
appliances/heat pump, etc, then you still may want one if you have an
attached car garage. There are natural gas detectors too, but unless
you are smelling impaired, I think they are optional, as the gas odor
is very easily detectable.