Improve sheep (always hills) and copper (mainly only because I don't want to waste the charge to harvest it, so just mine it). Production is great.
Leave alone (neither harvest nor improve): bananas, fish, rice/wheat (unless Egypt), deer (if the base tile is good, aka wooded/rainforested hills or reefs or enriched flood plains then it is a good tile even unimproved... can be harvested later as needed or if the base tile is crap). Wheat on flood plains especially... a farm yields a measly 1 food and causes you to potentially lose pop if it floods and it is pillaged.
Harvest: stone (empty mines are better due to apprenticeship; cannot spawn in woods or rainforest which makes it useless), crabs (lousy tile which cannot spawn on reef), cows (always flat grassland... terrible!).