There's few ways to go ahead with naval Soviet game.
1) Submarines for days, but then, Submarines are OP and always work, even if you were Saudi Arabia.
However for more interesting naval game, you could turn whole of Crimean coastline to a massive naval factory as you have plenty of building slots there even on day 1.
Researching 36 Battleships, Cruisers, and Battleship Converted Carrier comes next, then you just begin to produce screening cruisers, and few capital ships.
After this is done, you get to roleplay the Soviet Naval theorists before the start of operation Barbarossa, And build "light cruisers" that weight more than most countries heavy cruisers. And use these as Screening ships for your brand new navy you'll give Japanese a taste of revenge for the Battle of Tsushima.
Also of note is, to rush to take down Turkey, as having access through the straits is very important due to how naval AI works, and for some reason Paradox thought that Black Sea is the best spot for Russian naval constructions to spawn into.