Well, as a first, I'd like to welcome you to the game as others have done.
And then I'll answer the question the others haven't: As a general rule, you want the engine with the highest horsepower among those available. The extra speed is almost always more valuable than any weight savings or increased overheat times. This holds true for the vast majority of ship classes. For the O Class, I think it should be the DD Engine I (Heavy) that you choose.
Now, as to gunners, your gunners are indicated as being accuracy ones in the pack, but that only indicates their base stats, and does not preclude them from being classed otherwise. In general, you want to class all main gunners as reload every time. The reason is both stats have caps after which additional ability means nothing (they still get a level-based bonus, but that's fixed). This is FAR harder to attain for the reload stat than the accuracy one. For the RN, you have the added problems of the growth rate in the stat you didn't choose getting reduced, and you're locked in to whichever path you choose (you can't go one way, then the other). No other nation has either of these issues. As a result, if you choose accuracy, 109 vets and full experts (minimally decent crew) still won't get you to the reload cap by BB6. If you choose reload on the other hand, that same crew should have hit BOTH caps by the time you have a BB4, nearly 30 levels earlier.
There are a number of threads regarding ability calculation and caps in the Tips and Tactics section. Just search for "true ability," "[crew type] ability," and "[crew type] classing." Going to the Royal Navy forum and searching for "crew" is also recommended. Search content if titles don't show much, and remember that many of these will also discuss the merits of how to class sailors as well. Also note that some of the older threads may have some inaccuracies due to players not knowing about changes. As a new player, I recommend looking up advice for every sailor type as you get to the point you can class it up.
I have no idea about the "battleship" thing from the tutorial. I wouldn't worry about it.
Finally, the following: As you go up, the number of crew slots increases, and if you intend to go all the way to BB6, you will eventually need a total of 14 sailors. This should include your BO, 2-4 gunners, 1 recon pilot, 6-8 engis, and any remainder in repairers. It's a good idea to plan ahead since you'll constantly be needing to level up new crews. To that extent, many players advocate getting a second bridge operator (usually around CA to BB1 level) and taking it up an alternate ship line while leveling up additional crew.
