Ask for advice about battleship sim

I am not well educated in this particular genre, Pacific Storm comes to mind, played that game 10 or so years ago and enjoyed it. But its more strategy. Not sure how it plays today anyway. But currently this game is dirt cheap on Steam so might be worth a try.

World of Warships?
Although you can't call it Simulation without a guilty conscience ^^

Look up Battlestations:Midway/Pacific.

Kantai Collection /s

You can play these two games in arcade or simulation mode but it's specific because it's just submarines : Cold Waters and Silent hunter 5

Sorry i can't help you much because i enjoy arcade naval games, but i'm too stupid to play naval simulations... As an arcade fan, my favorite is Atlantic Fleet, turn-based naval battle, but if you don't like arcade you probably won't like it (in this one you fire and move fast and often and you aim manually but it's very assisted, but there are not just submarines, there are plenty of different surface battleships too). Victory at sea is real-time even more arcade and highly repetitive. And Battlestations Pacific/Midway are fun but arcade too.

If you search for naval sims, Cold Waters is probably a good bet, it's a sim so you spend more time searching and pursuing or hiding from ennemy at a very slow pace and taking into account distances, depth, trajectory and speed. Launching a torpedo is relatively rare and the conclusion of a long hunt. Be aware sometimes it requires not obvious knowledge, for example sound dispersion in relation to depth, this sort of things that the game doesn't explain you (but has a 56 pages manual and a helpful steam community)
Another possibility, (while i heard sims fans prefer Silent Hunter 4) Silent hunter 5 has an arcade mode very assisted and helpful but if you prefer you can search for ennemies ships manually using sonar and calculate torpedos course manually too, some mods give you more tools for that (ruler, compass) but if you don't know how you'll have to learn watching long youtube tutorials.

How about the Battleship game on the Xbox 360?

It's not 100% what you're looking for, but Fighting Steel, from 1999, might scratch your itch. It's supposedly quite realistic. Here's an ancient looking review for the game