Best places to live in London for Transport links

Anyone have any ideas about the best places to live in London? I'm from London but moved away to move to Portsmouth but am moving back.
I've always lived in South West with my family (Putney Battersea Stockwell). I will be moving back with my bf. So I'd like to be close to my parents but not SO close we're neighbours.

I want to live somewhere that has good transport, tube, overground and buses, so it's easy to get to where ever we work. It needs to be an easy and quick commute to Clapham Junction as thats where my Dr is (been my Dr since I was a baby, best Dr I've ever had and that's hard to find. I'm not giving her up).
But I'm mainly looking for somewhere that has quick and easy travel throughout the south west. And is relatively cheap, with a supermarket. 700 max for flatshare.

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