Don't be cheap. Look at part(s) that make an integrated system. Doesn't necessarily need to be from the same company, in fact sometimes the "mix" and "match" is ideal. It is for us.
nest thermostat or some similar ones will let you monitor temperatures remotely and control the thermostat if needed, along with warning you if temps are to high or low. Nest fire detectors will connect with it and warn you as well. Nest phone app lets you see inside temps as well as outside temp.
Ring/Nest cameras and alarm system will monitor inside and outside for safety. They also have water sensors to warn you of a leak.
Ring is easy to set up and the alarm system lets you give individuals a unique acess code and access ability so you know who and when someone is checking on the house.
Ring system and Nest thermostat has worked well for us.
In addition Leviton makes switches and outlets that are compatible with Nest and Ring and google home/alexa will randomly turn on lights etc. when it detects or you set to "away" in the evening from dusk till about 11pm to give the house a lived in look.
And when home the leviton app also will turn on lights when you come home, off when you leave. Nice at night to come home open the garage door, have garage lights come on and dining/living lights on when we walk in. Couple that with google/alexa and you can turn them on/off by voice or the app.
Downside is they quite while power is out, but our pieces have always come back up in sync when power/internet returns.