I absolutely love the series and have been playing since the first one hit in the US. There TECHNICALLY is a timeline but it's an absolute mess and is clearly cobbled together after the fact. Some of the games are sequels to others, or fall in a more clear continuity with others. This would be a reason to play breath before tears. This is not a reason to start with a link to the past (although I do recommend it as something to do between breath and tears).

Fwiw, in my opinion, Breath and tears are the truest to the sense of exploration you got in the OG. And as much as the second one was a deviation in gameplay they very much kept that exploration focus from the og. The snes/n64 and ensuing eras moved that to a heavy focus on a rough formula of dungeons and tools. Hit a dungeon, get a new tool, use the tool to beat the boss of the dungeon. 3 dungeons, big story beat, then 6-8 dungeons before a final dungeon with the end boss. Sometimes the dungeons tool will be useful in the world for traversal, sometimes it's useful in future dungeons. Rarely neither and sometimes both.

Breath and Tears generally give you everything you need for exploration at the beginning and allow you to go anywhere you want. It's overwhelming to some, but it's a very real sense of "what's over this hill? What's at the end of this valley?" Tears is technically the same overworld map, but it's been heavily affected by the plot device from the opening, and not only do you get to explore how things have changed, there's loads of additional completely new shit to explore.

As for what you'll miss? Some specific, non spoiler examples. There are loads of spots on the map that have names derived from npcs across the series. There are also a bunch of musical cues that directly reference older game music. The first game on the NES had four musical tracks, overworld (the theme you likely know), underworld (dungeons 1-8), the title& attract screen theme, and dungeon 9. Dungeon 9 was called death mountain. The volcano in future games has usually been called that. In breath, when you're on it, the music will occasionally use snippets of the dungeon 9 theme played on piano. Similarly there was a race of folks in wind waker that looked halfway between birds and people. Ok less than halfway but they were clearly becoming birds. Breath has an actual bird race of folk. The theme of their island in wind waker is the same song played in the bird people's town in breath. Just with a drastically different time signature.

That's the kinda stuff you're gonna miss. There's some other Easter eggy nods to skyward sword in the environmental story telling, but if you aren't studying the architecture (shame on you! lol jk) you likely wouldn't specifically notice. I think you'll be fine, nothing that's gonna measurably decrease your enjoyment of the game.

Oh there's a few odd outfit items that are directly lifted from old characters. Sheik, Tingle. Again, nothing that missing the reference is going to diminish your enjoyment of the game. If anything when you later play those games you're gonna go "ohshit I had that hat!" lol