Creating a Habitable Planet with 3 Moons

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TL;DR Summary: I’m worldbuilding for a novel I’d like to write. I’d like my planet to have 3 moons, and I’m curious how to develop the planet and moons in a scientifically sound way.

I apologize in advance if any of this doesn’t make sense or if terminology is way off or misused. This stuff is way above my head. But I’m trying to learn the factors I need to consider to develop a habitable planet with 3 moons.

The moons will be in a triangle around the planet, and they will have separate rotational orbits. The purpose here being that I need, on rare occasions, there to be multiple moons active (visible in the sky) simultaneously. Any combination of the three, including sometimes all of them. But I don’t know where to start determining sizes, orbits, rotational/orbit speed, distance from the habitable planet, etc. to ensure this is all scientifically believable.

Is there any advice or insight you guys can offer to help get me started in the right direction?
 
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Hi. I don't think you should worry too much about this. Any combination of orbits will periodically make the moons visible at the same time in the sky. Each orbit will have a different period, and this necessitates that every now and then the positions of the satellites will coincide - much like the planets in our solar system sometimes appear to 'meet' (i.e. conjunct) in the sky.
The constraints are that the moons can't be too close to the planet (this poses a variety of problems, mostly with extreme tides), too far (so as not to escape the gravitational influence of the planet) or too close to one another (so as not to pull one another out of their orbits on close approaches). Certainly not on identical orbits. They probably shouldn't be too big, as this poses stability concerns.
If your planet is approximately Earth-like, the star is approximately Sun-like, and the satellites are not excessively large, anything between about three times closer than the Moon and three times farther should be completely kosher to put the satellites within.

Your wording about the moons being 'in a triangle' around the planet raises my eyebrows a bit. I'm not sure what you mean, and the few ways I can imagine your intent wouldn't work.
Maybe describe your setup in more detail, so that we might scan it for anything outwardly implausible.

Btw, this post will likely be moved to the SF writing and world building section of the forum. Not to worry though.