A golden rule of getting into this industry is to never turn down a first job; as long as it's legal, go anywhere, do anything to get commercial experience in your logbook. You would be very fortunate to land a first job that allowed you to live at home, but once you have hours and experience, further opportunities start to open up, and it gets progressively easier to pick and choose a lifestyle and location that suit you.
Regarding 'a couple of hours' to LHR and LGW, have you factored in the M25 effect, or the 30 minutes required to get parked, catch the bus and get through security to the crewroom? Realistically, an hour's commute is as much as most people can manage.