The Lovers, the Dreamers, and Link
I don't think there are any Zelda games with a narrative as emotionally impactful as that of Link's Awakening. While the "it was all a dream" gimmick as a narrative mechanic is often derided as a total copout, and rightfully so, here it works in a way that really toys with your role as hero. Completing your quest (and in turn waking from your dream) means destroying the island you've helped save and erasing the relationships you've forged with the island's many inhabitants (of which there are many funny, lively characters). Not only will the bosses toy with your emotions upon their demise, but the "dream" mechanic allowed for the developers to get weird with Zelda in a way that Nintendo rarely allows. Mario, Yoshi, and Kirby all make cameo appearances. Confused village children make meta-references to gameplay. The most shocking creative decision would have to be the absence of Princess Zelda and A Number One villain Ganon. It's odd, but as Breath of the Wild has shown, often the "least Zelda" Zelda games in the series can be some of the best. Link's Awakening proves that theory as well.
It's closest cousin in the console Zelda games would be its immediate predecessor, A Link to the Past. The Gameboy's limited face buttons make for an annoying equipment interface (you'll be swapping items/weapons A LOT), but the core gameplay is quite similar to its SNES counterpart. It's also an impressively large world for a Gameboy game, and no part of the map can go unexplored. The main item swap sidequest that many Zelda games have is tied directly to the game's narrative and integral to figuring out the puzzle of the final dungeon. This may prove frustrating to new players, but phone booth hints from town elder Ulrira are actually quite helpful if you need a gentle shove in one direction or another.
The game can prove to be challenging in certain spots (I died no more than a dozen times), but never feels cheap. Its dungeons rival some of the best in the series, especially with regards to scope. Only once did I get truly stuck (in the final dungeon before the Egg). In both combat and puzzle solving, the challenge feels just right for a Zelda game.
If you've skipped over the portable Zelda games in the past or are looking for a reason to revisit this one, I recommend it as one of the finest Zelda games there is. On some days, I may tell you that it's my absolute favorite, but my heart constantly jockeys between this, Ocarina of Time, and Breath of the Wild.