The council training is pretty good. I used it a few years back to help me get more comfortable riding on London roads when I wanted to start commuting and now I do it year-round. A friend learned from scratch somewhere - nr Islington I think - and although she's not really kept it up, she can now at least get around Richmond Park slowly.
Forest Hill to Paddington wouldn't be all that bad. It's a fairly flat route - at least once you're out of FH! I'd probably go through Dulwich to Herne Hill and then to Stockwell. Then cut off towards Battersea Bridge, go up Sloane St and cut through Hyde Park.
However, to get back on topic, trains into Charing Cross would be handy. I miss that direct route into the Strand... the Jubilee line via Canada Water gets close but not enough if you're in a hurry.