Welcome to the forum, TwoFistedSarge!
To avoid confusion when it comes to the Conduct Combat Phase it is recommended to stick closely to the sequence defined by the rulebook:
1. Strategic Bombing Raids
2. Amphiboius Assaults
3. General Combat
The General Combat Sequence consists of seven steps:
1. Place units along the battle strip
2. Submarine surprise strike or submerge (sea battles only)
3. Attacking units fire
4. Defending units fire
5. Remove defender’s casualties
6. Press attack or retreat
7. Conclude combat
From this you see that submarine’s fire is actually part of the general combat.
Attacking and defending Submarines fire their surprise strike in step 2.
All other attacking and defending units fire in step 3 and 4.
Every attacking unit scores a hit when the die result is equal or lower than the attack value.
Every defending unit scores a hit when the die result is equal or lower than the defense value.
But units do not shoot at a specific target (if not one on one). It is always the opponent who decides which units are taken out.
After the attacking player has rolled for all attacking units, the defender chooses one
unit for each hit scored and moves it behind the casualty strip.
However these casualties can fire back (if not hit by submarine’s surprise strike) in step 4.
The attacker then chooses his units as casualties. Those units are removed from the game then as well as the defender’s casualties.
When choosing casualties be sure to assign hits correctly. So a submarine for example cannot hit an air unit.
If a submarine attacks a cruiser and a fighter and scores a hit, the defender must assign the hit to the cruiser.
If no special rules like this apply, the opponents are free to choose what units are taken out.
I cannot cover all the details of the Conduct Combat Phase and their sequences here so please ask back if I missed to answer parts of your questions.
HTH :-)