Well guys as a person that has been in the HVAC industry for over 30 years, I have to chuckle a bit as I read some of the responses. Started out as a repair tech and now I manage a branch for a large HVAC/R wholesaler. The nest is ok for a retail thermostat. Ecobee a bit more advanced but still a retail version with a few more bells and whistles. If you want a basic multistage thermostat with wifi take a look at the Emerson White Rodgers Sensi. For the money one of the best out there just a bit over $100 but very solid and will outlast the nest by far.
If you want better control look at the Honeywell line with Redlink capabilities very solid thermostat with more options than most would need. The biggest obstacle is the best thermostats are not available in the retail market. They must be purchased through a dealer from a wholesaler. As for any 2 stage cooling equipment you are not buying it for savings ie lower operating cost. It is all about comfort longer running time = less humidity = a more comfortable house at a higher temperature. Almost every 2 stage A/C is only unloading 40% or so of the load but still cost the same to operate the compressor. Unless you get one of the newest variable frequency drive units wich are rare in a whole house A/C for now anyway.
As for the term hydronic that refers to any system that uses hot water as its source of heat. Boilers or maybe Geo Thermal water to water heat pumps. And then there are the many manufacturers brands of communication thermostats that are only compatible with their equipment but are made by the major heating control companies. Honeywell, Emerson White Rodgers, and even Ecobee. But anything you buy at the retail level is pared down and has a shorter warranty period than what your contractor can buy.
I a not trying to be a smart eleck but just wanted to pass along some information that I have a lot of experience in. The Nest built in lithium batteries that will die out on you. Eco Bee ok but not as good as you will get from your heating contractor. Emerson White Rodgers Sensi great stat same as your contractor can get very few warranty issues actually 0 since they came out for my store anyway. Even better Honeywells line of thermostats you just need to pick the one that has the features you want.