Spying costs 1 AP no matter what the type.
Spying effectiveness is controlled by your spy level in your institute building. If your opponent's spy is a higher level you may not be able to see everything your target has.
Previus Spying results are avialable in your Mail.
When Spying on buildings you get information about the current resources the other player has as well as the level of all the buildings that are on the planet you chose to spy on. In terms of choosing which enemy planet to attack the most important building is the Emplacement. This is becuase this building is the only one that you interact with directly in a PvP battle
When you Spy on Heroes it does not matter which one of the players planets you have selected. You get information on the types and levels of the opponents heroes as well as their War and Command stats and which skills they have equiped.
When you use Army Spy, it does not matter which one of the players planets you click on.
You see the number and Class of ships the player has equipped.
You can also see which weapons and devices the ships have equipped. Comined with Spy Tech, you can gather very detailed information as to what threat the ships pose to you and you can choose which ships you want to send out against them