A tough question.
Super Nintendo: Earthbound. A personal favorite, partially from nostalgia. Enjoys all the little mechanics (especially rolling hitpoint damage) and the world in general.
Replays it from time to time still. Plans to soon, actually. Cannot figure out a fun challenge to add. Refrained from equipping anything last time. Maybe "no withdrawals or egg farming"?
N64: Paper Mario. Views this as one of the weaker game systems. Rose as the best choice, despite not even being the best Paper Mario. Highlights its leveling system. Chooses between Hitpoints, Flower Points (see: mana), and Badge Points (see: special attacks and passive effects). May opt to never increase one. Considers it a tough choice, as well as a good source of replayability.
Gamecube: Tales of Symphonia. Loved the story and characters. Was also drawn in the battle system. Never played anything like it before. Became more special for being "the first".
Was a rough choice here. Beat out Paper Mario: The Thousand Year Door and Fire Emblem: Path of Radiance mostly because of other entries in those series being selected elsewhere.
Wii: Kirby's Return to Dreamland. Faced a situation much like the N64's. Cared less about this system. Prefers at least one other Kirby game (Kirby Super Star) to this. Earns the spot for its [True] Arena. Breezed through the main game. Ramps up for the Arena and True Arena. Brought that desired difficulty and then some. Describes it as the purest gaming moment in a long time. (Applied more to Planet Robobot on the 3DS. Fits this game well too, though.)
Switch: Rune Factory 4: Special? Liked one Harvest Moon game before. Cannot describe why balancing farming, making cash, and speaking with villagers was interesting. Cranked it up in this game. Adds combat and crafting into the mix. Provides more direction.
Completed it only once versus three times each for both runner-ups (Pokemon Sword and Fire Emblem: Three Houses). Might not hold up as well the second time around. (Will likely revisit it after Earthbound.)
Game Boy Color: Pokemon Crystal. Calls it the best generation. Introduced a lot of good Pokemon and features into the series. Has not replayed it in ages, admittedly. Might balk at the missing features like abilities and physical/special split. Outpaces the competition easily, though.
Game Boy Advance: Golden Sun: The Lost Age. Separates itself from others with its Djinn system. Affects the equipped character's spells and stats. Usually stuck with same-type Djinns. Presents an interesting option for additional playthroughs.
Remembers very little difference, gameplay-wise, between this and the original. Figured the second half would be more refined.
DS: Chrono Trigger. Yes, a port. Added no good new content. Savors this game's story and music that much. Edged out The World Ends With You, despite also being a stellar game. Thought about which would be more fun to replay. Chose Chrono Trigger.
3DS: Fire Emblem: Awakening. Bridges the gap between older and newer Fire Emblems. Takes the stronger parts of the old games (an interesting story for the first third) and the new games (skill decisions, reclassing, and strong support mechanics). May not be the best example in the series of individual mechanics, but the most preferred package.
PC: Terraria. Permits more creativity than the other games here with building. Enjoys constructing arenas for bosses. Views it as half the battle and just as rewarding as executing a strategy while fighting a boss. Presents plenty of difficulty and interesting weapons. Created clear avenues for different playstyles (melee, ranged, caster, and summoner), and therefore, an easy reason to replay it. Offers even more through mods.
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Picked mostly favorites of each system. Valued replayability and series variety. Made some possible decisions easier. Overwhelmingly selected roleplaying games, unsurprisingly. Feels happy with this list. Realized how fun it might be to replay some of these while making the list (on top of the ones already planned above).