For an individual appliance you need to likely measure power factor, volts, watts and watt/hours, so you can for example measure the power used by your freezer over a set times and from that calculate the kWh/annum to see if it is working as it should or if there is a fault like loss of some of the gas.
However as a whole house it may highlight an unexplained draw where some thing is left on, but all you need to know is something is drawing current when it should not, you really don't need to know how much, just that something is working when it should not be.
The plug in meter does help to chose what you do, for example a Sky box uses around 12 Wh to be able to update program change information, you have to decide if worth the cost to have it auto change recoding times when the programming times change, but for most of the time you can see what some thing uses by simply reading the label, very few items need to be recorded using an energy meter and even when they are a general meter that measures all tells you very little of use.
I know like everyone else if I turn my heating down it will save money, knowing if I drop the temperature by one degree it will save me £X will help me decide if I want to live in a cool house or a warm house. However to measure not only do you need to measure gas used, but also wind direction and speed and outside temperature I am sure I could get a weather station and do that, however I really can't be bothered.