Oh i think you definitely need to select the spell and level, since you cast it using a spell slot, if any. Compared to the Attack action, that don't need to specify which type of attack (melee or ranged) and with what weapon will be used, Readying a spell need to commit a little more. But in any case, targeting shouldn't come up until you take the reaction to complete your readied action.

You have to give some indication as to the target, rather than a specific target.

e.g. the first enemy to step in through the door, or the first enemy I see coming round the corner of the building, the front of the ship when it gets within range.

The spell is cast during your own turn, so everything about the spell, such as level and metamagic that affects the casting would also need to be specified at that time.

Not necessarily, it could be "when the door open, i do attack" or "when the ship come into range, i cast Fireball"

RAW there's no need to specify a target for a readied action.  You only need to specify the perceivable trigger and the action.

For perceivable, we take the definition  "perceivable - capable of being perceived especially by sight or hearing" which simply means that the trigger must be something that the character can be aware of when it happens.  I could put "When someone waves at me" but I couldn't put "When someone in that magical Darkness waves at me" because I'd be unable to perceive the trigger.  I could say "When someone waves at me" then another character casts "Invisible" on themselves and waves at me, but I'd be unable to use it as the trigger because I can't perceive them waving.  I could also say "When someone waves at me" then get struck with the "Blindness" condition before my next turn and be completely incapable of perceiving the trigger.

We're not told to specify a "foreseeable" or "predictable" trigger or that the target of our action must be relatable to the trigger.

We're also able to choose which trigger to use our readied action on.  We aren't forced to use our readied action on only the first trigger unless we specified "the first" in our trigger description, and even then we can choose to ignore all triggers and forgo using the readied action at all.

I might look into a room and say TRIGGER: "When something comes towards me", ACTION: "throw a fireball".

I see a goblin enter the room but don't use it for the trigger. Another goblin, and another and another, all the while holding my reaction until I think there's enough goblins in the room.  Then, suddenly a hobgoblin enters the room with the princess I'm supposed to rescue.  I decide to just keep that fireball in check... Then a Manticore flies out of a open roof ruin behind us and into the air directly above me.  I figure I have my target until the smug DM tells me it didn't move towards me at any point, only from a space of equal distance behind to a space of equal distance above.  I grumble until the DM announces the Manticore is attacking with it's tail spikes and as those spikes are "something and rain down towards me I rejoice and release a fireball towards it.

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However, I do believe that DMs should look out for uses of the Ready action that attempt to exploit it too far with open ended wording.  Some DMs don't like the idea of a caster avoiding counterspell by moving around a corner, casting the spell as a ready action, out of sight of the opponent, then moving around to "release" the spell.  Personally, I think its fine because it takes not only the caster's Action, but their Reaction until the next turn, also requiring the movement cost to get out of sight then back in sight rather than potentially moving somewhere more advantageous in position.