Attack vs defense priority in battle fleet clashes

Let's say two equal battle fleets, both containing heavy cruisers (CA) and destroyers (DD) clash. Ideally, as being screen vessels, the DDs are closest to the enemy fleet, the CAs are a bit farther out. I assume when the battle starts the DDs on both sides should normally start steaming towards the enemy at full speed to close the range for their torpedos.

I know tactics depend on specific situations and such, but what do you think is best in general:
1. Should DDs ignore the enemy DDs and continue steaming towards the enemy CAs (attack priority) or should they engage the enemy screen DDs that they pass by (defense priority)?
2. Should the CAs try to close the range to enemy CAs to target them (attack priority) or rather try to run away to keep enemy DDs out of torpedo range but still in their gun range so they can finish of enemy DDs first (defense priority)?

What do your ships do in similar situations?
Does anyone know what doctrines were used in similar situations in real life?

That is a difficult question. If your DD's ignore enemy DD's, then they can close to torp your cruisers.
I am unsure of the historical tactics; but for me, I propose a mixed approach.
I would absolutely go full speed ahead on DD's.
I would bang away at the enemy DD's on the way by, but I would save torps for the enemy heavies.
I might have 1 or 2 of my DD's stay & try to tie up the enemy screen while the rest dash for the cruisers & larger ships in the back.

After quite a few games we played with this ruleset it seemed to us that charging with DDs is the best approach. DDs seem simply too difficult to hit with guns and torpedos are deadly.

However, we noticed that in other rulesets (such as General Quarters) this may not be the best approach: unless DDs are overwhelming the defenders in numbers (or attack at night), at mid range the DDs will be demolished by big guns before they can get into torpedo range.

I am currently reading the book "Last stand of the tin can sailors" which is about the battle off Samar. That is exactly what is described in the book.
Japanese Battleships & Heavy Cruisers firing at US destroyers & Destroyer Escorts at close range & missing many of their shots due to the speed, size & evasive maneuvers of the DD's.