Is it better to us my macbook air in battery mode at home or in charging mode?

The battery will last longer if not being used -- but it should be used some. A common recommendation is that it should be used a minimum of one cycle per month without ever being completely or heavily discharged. A cycle would be to use it until it is about 50% discharged twice during a month or 50% once and 75% twice for example. Mostly I just use mine in a way that is convenient for what I need to do,

The two techs I work with always say to use it on battery a couple times a month but never to fully discharge it. When the OS warns you are on emergency battery power either turn it off or plug it in. (It is okay to use while the battery is recharging)