Can I use the wish spell to have superior influence over all metallic dragons? Or do I just limit myself to one specific color of dragon? And can I make myself ruler of that color of dragon?
You could try, but you're not guaranteed to get it
The wish spell lets you make any request to your DM, however they need not fulfil it exactly, or in a way that is satisfactory to you:
You might be able to achieve something beyond the scope of the above examples. State your wish to the GM as precisely as possible. The GM has great latitude in ruling what occurs in such an instance; the greater the wish, the greater the likelihood that something goes wrong. This spell might simply fail, the effect you desire might only be partly achieved, or you might suffer some unforeseen consequence as a result of how you worded the wish.
From a DM's point of view, any usage of wish which attempts to "break" the game in some manner; such as granting a player an immense amount of power, would not be granted. Either they would simply let it fail, or twist your words so that what you are granted is actually detrimental to you, or a major unforeseen cost.
For your specific question, asking to be made into the ruler of Dragons, your DM might turn you into (or trap you inside) Tiamat (who is trapped The Nine Hells and is the rightful ruler of all dragons in Her own mind), or something else dependent on their creativity.
It's up to your DM, but it's unlikely to work.
It could work, if your DM allowed it, but the guidelines suggest that it's unlikely to succeed in the way you hoped.
Player's Handbook, p.289:
You might be able to achieve something beyond the scope of the above examples. State your wish to the DM as precisely as possible. The DM has great latitude in ruling what occurs in such an instance; the greater the likelihood that something goes wrong. The spell might simply fail, the effect your desire might only be partly achieved, you might suffer some unforseen consequences as a result of how you worded the wish. For example, wishing that a villain were dead might propel you foward in time to a period when that villain is no longer alive, effectively removing you from the game. Similarly, wishing for a legendary magic item or artifact might instantly transport you to the prescence of the item's current owner.
The ability you're asking for is approximately equivalent to the Orb of Dragonkind, an artifact-level item, which allows you to call dragons; in fact, if you want the ability to freely command dragons, you're asking for even greater power than the D&D 5e version of the Orbs. The guidelines given in the wish spell suggest that wishing for this kind of power is likely to fail or result in unexpected results.
For example, the wish might do the following:
- Send you to another world where there are very few dragons, or none
- Make you nominally the ruler of dragons, but having no real authority or power, so all dragons in the world quickly decide to violently despose you
- Make you nominally the ruler of all dragons, the only benefit of which is that all dragons refer to you as "Your Highness" (no other effect)
- Make you the ruler of The Dragons, which turns out to be a minor thieves' guild in Waterdeep consisting of three incompetent oafs who owe a lot of money to the Xanathar
- Make you the ruler of red dragons... but only two tiny red pseudodragons, who are now your pets
Traditionally, DMs would handle unreasonably powerful applications of wish by intentionally interpreting the request too literally, without actually giving the player what they expected. If you wished for a million gold pieces, you got a million specks of gold dust, or perhaps you were crushed beneath a million gold pieces, or the gold came from the royal vault and now you're desperately trying to launder it before the king finds out...