As mentioned in comments, avarice blade on trynd, GP, Nocturne, or even Garen can work. Other than that, it's quite a niche item and isn't very cost-effective for other champs. They took out HoG, which was the only GP/10 item that worked well on EVERY champ :( . Philo stone works well on most tops that use mana, as well as EVERY support. As mentioned before, if you are planning on upgrading to either morelonomicon or DFG, Kage's lucky pick is worthwhile to get early on your AP Carry. (edit: just noticed it's part of athene's unholy grail while i was playing a match with Galio, good pick up for him, as well.)
Support should ALWAYS have a philo, as later game every support should have shurelya's.
It should be noted that GP/10 isn't common on jungler, with the exception of mana hungry ones, like Amumumu or Maokai, which benefit greatly from Philo, and then even moreso from Shurelya's later game.
SK gaming did a great write up on GP/10s here.
As for specific questions in the OP: Good time is earliest possible, I.E. I rush them before boots when i'm support. Later game they are generally a waste of inventory slot. Selling them isn't as cost effective as upgrading them to something relevant for your champion. Only time i would sell them is if I went something like 2 philo stones, upgrade one to shurelyas, sell the second one to get something else...