What tiles are the best to put GP improvements on?
And when do you start popping GP instead of using on a tile?
Tiles:
Usually on a bonus resource that has a weak improvement. Wheat, rice, or corn are commonly good picks. Empty grassland or plains get filled up eventually too, and towns can go along roads between cities.
Great Writer:
4 great works should be enough to theme Oxford University and 1 amphitheater. Then I get the instant boost.
Artist:
Great works early on, then drop a couple for golden age points as needed.
Musician:
Great works for most of the game. By the like industrial era the concert mission is better but they take a long time to travel and its hard to get a window without war to use it.
Engineer:
I usually plant like 3? Nothing wrong with immediately using these guys early game though.
Scientist:
If taking rationalism, I plant every guy until I reach the extra yields in rationalism. Otherwise I'll start popping after reaching industrial era. Nothing wrong with popping a bit earlier if you want a really key tech.
Merchant:
Towns aren't too important and the instant gold can make a big difference. However if you take the +4 faith +4 science to great person tiles then I probably plant 4 or 5 as towns.
EDIT: Another thing you can do is if a great person is coming and you are planning to chop jungle/forest, plan to use him to chop instantly