I'm writting a story that revolves around a bit of space exploration, but I have come to a problem: Should I make the system heliocentric, like our own system, or Equuscentric, that would be closer to the show mythology?

Either works, it all depends on the story and what it needs.

Due to the show's celestial patterns, I would recommend Equuscentric, as that is more canonical. However, due to magic's existence in the show, pretty much anything is possible, including Celestia trolling by changing it periodically.

4740223 Equuscentric, and make sure you come up with an explanation for why the moon projects darkness the same way the sun makes light (see season 4 premier).

I would say heliocentric, because in a little story I'm making, a space exploration team finds Equestria, and I guess I kinda ruin the shows canon and make it a 'myth' that Celestia and Luna raise the sun and moon, and that the planet is.actually heliocentric.

Why not both? Personally, I favour the theory that the actual sun of that system is long dead, and the one Celestia controls is an artificial satellite.

But yeah, like others said it's completely up to you. Whatever works for your story best is preferable, and if happens to contradict canon a bit too much, give it the AU tag.

I've always imagined it as the "Sun" actually being a magically burning moon-sized object.

Whatever fits the story you want to tell better!