There's pretty much no interconnecting narrative (it's not Mass Effect), and there's only a handful of reoccurring Links.
The five games I personally recommend playing are Twilight Princess, The Wind Waker, Majora's Mask 3D, Link's Awakening (Switch, but DX via 3DS Virtual Console is a good choice too), and A Link Between Worlds.
The rest of the games tend to have frustrating gimmicks and design decisions that just kill my personal interest - Skyward Sword has shield fragility, far-too-limited Pouch, repetition, dysfunctional motion controls, stamina, repetition, slow flying, timed Tear-collecting sequences with reset conditions, and repetition. The Oracle duo (via 3DS VC) are large games heavily limited by the GBC; they seriously need the remake treatment (Link's Awakening DX managed to be fun despite the GBC due to its simplicity). The Nintendo DS duo have that stupid stylus restriction, despite the handheld having buttons galore; idiotic designers...Ocarina of Time has an overwhelmingly slow beginning, and Link to the Past is archaic and has enemies that deal far too much damage in the Dark World.
Oh, and Breath of the Wild...I heavily recommend against buying and playing this disaster. Equipment fragility, stamina, resource grinding, slow and tedious world traversal, bland and empty open-world, repetitive shrines, overpowered enemies, and a dearth of tools compared to actual Legend of Zelda games. Oh, and slow and clunky combat.
I managed to slog my way through Skyward Sword a handful of times over the years, despite that shitstain's many flaws and anger-inducers. I only managed to play a few hours of Breath of the Wild before I got absolutely sick of it, ejected the preowned cartridge, and threw it in a drawer somewhere. Almost nothing redeemable here.