First, please understand that the Trinity is itself an analogy. It is an anthropomorphic description of God’s three masculine hypostases. Assuming you’re not familiar with this, you can either invest time into studying and contemplating this, which may or may not reveal and confirm the Truth of the Trinity to you, or simply accept it as given. In any case, it is possible in principle to understand the Trinity, so in that sense it should not be labeled an “inaccessible mystery”, as some do.
Having said that, on to your question. You’re asking for an analogy for an analogy, and you’ve offered three examples. The first is by far the least adequate, because the Trinity is not a collection within which three persons relate to each other. The second is much better, because it makes it clear that there is only one God, and compares His hypostases to roles. This isn’t perfect, but it’s acceptable (in my opinion) as an easy-to-understand analogy. The third is alright because it makes it clear that God’s substance is the same in all three persons, but unfortunately it is impersonal and suggests that God goes through transitions in order to become one or another of the Persons – which is not accurate.
Want another one? Think of God’s substance as Light. The Father is then the sun, the Son is a reflected image of that sun in e.g. a mirror, and the Holy Spirit is a ray of light coming from the Sun, reflecting off the mirror, and then warming something. Personally I like this one because it too retains the notion of substance, makes it clear that the Son is an image of the Father, that the Holy Spirit proceeds from the Father through the son, and that the Holy Spirit ultimately works a transformation, analogous to the role of light in photosynthesis. But this one too is not perfect, because it too is not personal, and does not elucidate the begetting of the Son. But perhaps it helps.