I lived in Barnet for several months in 2013, it's a reasonably affluent area, green leafy suburbs. High rent, for the most part. From quickly looking at income data, the surrounding areas are relatively heterogenous though, so you'll most likely find a cheap place nearby. There's plenty of bus services to and from the town centre and the fare doesn't scale with distance so living elsewhere might work very well for you. As I recall there were plenty of cycle paths, so biking might work too if you're at that kind of distance. If you end up living to the south of Barnet, don't be tempted to use the Tube just because it's there - even an annual pass just for Zone 4-5 is more expensive than an annual bus pass for the whole of London.