My tenant changed out the thermostat in the unit (a lease violation) which caused the heat in the unit to not function.

Typically this problem occurs when you have the thermostat on the main floor, where most of the air flow is needed.

(I did it successfully)6am call because there is no hot water, thermostat burned out in the middle of the night.There's other stories I have too and I'm a noob at landlording, I've only had tenants for 3 months.So realize it's like MikeOH says it's not nearly as easy as the gurus say.

Maybe getting a quote for a 90% efficiency unit if you are paying for utilities or get an 80% unit anyway and put a thermostat lockbox over the thermostat and leave it at minimum of whatever the local code requires for heat during the winter for a rental unit.

Which means in the case of a furnace they will move the thermostat and see if it kicks on.

One suggestion would be to move the thermostat to an area the does not get as much heat.  

Lastly, the entire home we have decided to make "smart" and all locks, locks, thermostat, towel warmer, and mood lighting will be controlled via phones or computer.

Lock the thermostat so tenants do not have ability to change temp settings as well.

Also what's the best cheapest digital thermostat I can buy?

As for the furnace you are best to lock the thermostat.