So situation come up, in a battle lets say we have 2 ships with same PS.

Then both ships see 2 targets, of which 1 is same. (Does not matter much)

So my shooting round begins, so can i measure both ship ranged to enemy ship, then decide which is better to shot first, then shot with that? Or do i need to choose 1 of my ships, and then i measure ranges from that ship, shot and then move to another ship?

How it is handled?

As heard both oppinions, that you can measure for both ships and pick bets to shot from first and you need to declare who is shooting and measure just from that till you move to next ship shooting.

You have three times you can measure range per the FAQ :

Players may only measure range and/or use the range ruler to determine
whether a ship is inside or outside of a firing arc at the following times:
•
When a ship becomes the active ship during the combat phase, the active
player can measure range from the active ship to any enemy ships before
declaring one as its target.
•
When a player declares a ship’s ability that requires another ship (or ships)
to be at a certain range, the player trying to resolve the ability can measure
range from their ship to any valid ships before resolving the ability.
•
After declaring the intended target of a target lock action, the active player
may measure range to the intended target, and only to the intended target.

In this case, it's #1 and ONLY when that ship activates. In other words, make your best guess and pick one to activate first in the combat phase.

You have to choose a ship, measure with it (to any enemy ship on the board, including ones which are out of arc, if you want to), shoot with it, then choose another.

Thank you very much