Often, supports, due to their nature as 0cs champions, run out of gold to purchase both wards, oracles, and the items necessary to survive. If a team's support is weak either from lack of gold or being denied experience, then it can be extremely dangerous for the support to go anywhere on the map where enemy wards might be. This can be rectified by giving the support an escort, but even so, the support will typically be weak, and runs the risk of getting stunned, snared, or even one-shotted by champions with strong burst damage.
During the early game, oracles is actually much more potent on a jungler than on the support because the support will typically be confined to bot lane protecting the carry, with an occasional trip to clear and ward dragon. The jungler, on the other hand, by nature of the role, will be wandering the map and covering significantly more ground. Junglers are also, as a rule, tankier than supports. While Alistar, taric, and nunu all have the potential to get fairly tanky, they will still typically be easier to kill than almost any jungler.
During the mid and late game, it is often better to have the oracles on the support simply because if the enemy chooses to use their burst on the support during a team fight, then the rest of the team can typically take advantage of the enemy's poor target selection. Killing the jungler, however, has far greater consequences for team fights, since it makes it nearly impossible to contest baron or dragon without smite.
This is entirely situational. If their AD carry is out of place and you have the window to take him out then by all means do so. But if he is in the back you will just get yourself killed. I think this is common sense. You will have to stay disciplined and act if you have the window of opportunity.
Otherwise just dps the one who is in your range. Prioritize squishies over tanks but if you only have a tank in range then hit him. Some damage is better than no damage.
Best Answer
The first rule for that is always: It's better anyone gets the kill than noone gets the kill, so don't risk someone escaping with 5hp just because you thought the other guy had his gap closer ready when he hadn't.
The second rule would be: Know the item builds of your teammates.
Who gets the kills depends on which champion is more item dependant.
As an example if you are a jungle bruiser like Lee Sin you are usually more item dependant than most tanks in the top lane, so you can make better use of the extra gold. If you are a jungle tank like Nautilus and the top lane is a bruiser, let him take the kill if the opportunity arises, the extra gold will help him win the lane.
As an exception, if the tank top laner requires an early item for higher efficiency, for example Tear or Manamune on Yorick, leave the kills to them until they have completed that item.
For mid and bot, always try to leave them the kills if there is no chance for the opponent to escape.