>>12078021
The release order is
MOTHER
MOTHER 2 Gyiyg no Gyakushuu (released in English as EarthBound)
MOTHER 3
The game's story's are largely standalone, but they have some connections. The connections between MOTHER and EarthBound are much weaker than the connections between EarthBound and MOTHER 3. MOTHER has some Famicom era JRPG jank, so a lot of people recommend skipping it, starting with EarthBound, and checking it out after if you really like the rest of the series.
Depending on whether or not you are willing to put up with a Famicom JRPG, the recommended order is either
EarthBound, MOTHER 3, MOTHER
or
MOTHER, EarthBound, MOTHER 3
The connections between games is weak enough that if you REALLY want, you can start with MOTHER 3 and it won't ruin the game or anything.
Regarding MOTHER, the game has two different translations. One by Phil Sandhop, and one by Clyde Mandelin (the person who did the MOTHER 3 translation). The one by Sandhop is the official Nintendo translation. It was completed but not released in the 90s, leaked online in the early 2000s, and then officially released in 2015 as a Virtual Console game under the title "EarthBound Beginnings." The title screen calls it "Earth Bound." If you play the ROM from any standard ROM set or from an official Nintendo source, this is the translation you will be using. Mandelin's translation is a patch you can download here:
https://www.romhacking.net/hacks/5923/
Having played both of them, I strongly prefer Mandelin's translation, so I recommend you play with that. Sandhop's translation loses much of the game's humor and is very much a product of the late 80s/early 90s.
MOTHER 1 and EarthBound have GBA ports released under the title MOTHER 1+2, but these versions suck and I recommend you ignore them.