The way a character thinks of a ship tells a lot about the relationship between the character and the ship. For example:
- Someone who thinks of the ship as an inanimate tool will naturally tend to refer to it as an "it"
- Thinking of a ship as a "she" implies a more sentimental approach, pretending that the ship is an individual, maybe even actually considering it to be a full person. This is common because it's been common for sailors to ascribe personality, desires, and a sort of free will to the ship.
- But your own setting could have its own customs and idiosyncrasies! Maybe in your world, ships are individuals with personalities, but they're bizarre and otherworldly, so people think of them as individuals but not female (or male), and use "it".
Generally speaking, that's where variation in reference comes from - different ways of thinking of ships. Either form of reference you choose should be fine and unobtrusive, as long as you use it consistently (throughout the book, or per character). If they relation between people and ships isn't interesting or important to you, just choose one and go with that. If it is, then figure out what best suits your world and your characters. Either way, recall that the choice of how to refer to the ship is individual - different characters can refer to the ship differently; but a single character will generally stick to the same reference method at all times.
Regarding the last option you suggested, I would advise you to avoid alternating the reference between usages of the name and plain old "ship". This is not common or proper - and you'll notice it precisely undermines my central point here, which is that the way people feel about the ship as an "individual" affects the way they refer to it. Since their feelings for the ship - their awareness of it - stays consistent, the way that they refer to it will stay consistent as well.