We wouldn't need more than 2 bedrooms. We would be leaning toward a house but a flat isn't out of the question. We would definitely want to be near a park for the dogs. Easy access to the buses and tube are a must. We're not planning on a car so parking is not a need.
I've been at rightmove, prime location, etc. I've heard good things about Putney, hammersmith, etc but am really having a hard time knowing which borough of London is a good fit. We're looking for an affordable borough that's more laid back, quiet, and walkable.