Okay, so something might need to be addressed. A lot of people are suggesting that, for multiple reasons, you should skip Metroid: Other M.
I agree - analogs to Sonic 06 are not off the mark, though the game isn't broken like that one is. But something you need to know is that a lot of the issues people had with Other M started in other games in the series who tried to set those events up retroactively. Namely Zero Mission and especially Fusion.
Because of this, I can't impress enough how, if you can stomach it, you should play the games in release order instead. Zero Mission is objectively superior to Metroid 1, there's no debating that, but Zero Mission adds story elements retroactively that directly influenced the events of Other M.
Fusion is unavoidable and the worst offender of this, so play it last. For Samus Returns, it's another thing where I really don't trust the producer Sakamoto to just leave that game alone and try to preserve it, so you're likely better off playing the original. Your entire view of who Samus is as a character will be shaped by the order you play the games in, and if you play them in "remake" order, you WILL get the Other M view in your head by design, and that is both an inferior and less authentic Samus.
So while everyone else suggests Zero Mission, Samus Returns, Super Metroid, and Fusion, I suggest Metroid 1, Metroid 2, Super Metroid, Metroid Prime, Metroid Prime 2, Metroid Prime 3, Zero Mission, Samus Returns, and then Fusion.
Prime 1+2 are far more authentic to the original design philosophy around Samus than any game after Super Metroid was. 3 is where it starts to get influenced, at least aesthetically, by the changes in the main universe, while also being where Tanabe's obsession with turning Metroid into a Halo clone started. (The latter really started with Prime 2, but that was just because of the optional multiplayer and some intrusive story bits.)