I am the lead service tech at one of the larger companies in my area. I deal with these stats all the time.
There is nothing about a smart thermostat in it self that will save you money. Perticularly if you heat with gas.
A GOOD programable stat yes, if you program it and leave the program alone. Having the ability to change settings remotely suggests you intend to make regular changes to temperature settings.
Simple facts that sales folks dont talk about. The nest was purchased by yahoo or google (dont recall exactly which). They use wi fi to track your behavior to market products to you. The outdoor temperature they display is not the temperture out side your house. They dont allow a tech to customize operation settings to suit the equipent that you own. And they glich often. If you have less than perfict wi fi good luck. If you dont have wi fi and just like how they look, it wont get software updates.
I was ofered one for free and did not take it.
They are toys for most people. There are folks with situations, like grandma's house that remote access by you could be very convenient or a vacation home far away would let you see that equipment has failed.
Some send equipment notification that drive people nuts. The notifications are usually random nuisance faults that are meaningless.
If you must the honeywell has been the most trouble free and has had the best customer satisfaction, from my customers.
And if you are talking to the guy that works for lowes, depot, or you local mega store he is very under informed. If there is a guy thete representing a brand of equipment , carrier/trane ect. Only talk to him, he dont really work there, hes an outside rep.
As far as loacation of the stat. It should never be on an outside wall. And it should be near an air returnso that it reads temperture or the air being pulled back to the furnace/air handler. Your room may or may not have good air flow. To much or too little air flow and the rest of the house suffers. If it has averaging capabilities that is a good tool but you'll probably meet me when you call to have it setup correctly , about $ 200. From the co. I work for
To summarize 25 yrs a tech, have taught in apprenticeship, I hold every related certification, and state license, including N.A.T.E., and believe they are a scam.