Are you supposed to be on standby when home??
No you are not on standby when at home... 6 days On, 5 days OFF. But if your roster or your duty is to be on standby from home then the times mentioned above will apply.
Standby are not the common so perhaps you could get yourself a girlfriend who lives nearby your gateway in case you have some standby to do ?
On the other hand since nothing in terms of duty is predictable if you have a last minute change which becomes a SBY then you might have a problem.
An hour from a base/gateway for many companies is quite common too. NJE scheduling has to work for you before you join otherwise you will be disappointed.