No trains go from Baron's Court to Edgeware road (despite what the map tells you). You could change from Piccadilly to District there, and then change again at Earls Court.

Both Earl's Court and South Kensington require stairs to change. So I would just go with the shortest way and change at Earl's Court.

Of course you could catch the Heathrow Express or Connect which goes to Paddington which is pretty close to Edgeware road.