Do you intend to get moving in the mornings in the peak hours - before 9:30am Monday to Friday? Or travel on trains in the afternoon peak hours - 1645 to 1900?
If the first, peak time travelcards or Oyster fares will be required, adding lots of cost.
If the second, off-peak travelcards will not be valid on the train, but are valid on Overground, Underground and buses.
Denmark Hill is both quite convenient to the Overground loop, but much more difficult than many other places to get to the areas most tourists visit since the loop was completed last year. Fewer trains now run from there into London mainline stations.
As mentioned, wherever you are going you will have to change onto the tube or buses. Direct buses will not be much help from Denmark Hill. Although several of the buses go north of the River, and past some tourist attractions, but travel time will be long.