1) As others have said, yes. In fact, in many cases I would say get the remakes first, because in almost all cases they are better than the originals (unless you just want to go for nostalgia). I would also suggest getting the different versions of TP (motion control on Wii vs. traditional controls on either GCN or Wii U HD remaster). I know these boards are more for physical versions, but I thought I'd also point out that as far as I'm aware, there aren't any real digital-only exclusives, with a possible exception being the DSi/3DS "enhanced remake" of Four Swords. It has an exclusive single player mode (controlling 2 Links, similar to FSA on GCN) and two new bonus levels, however I think you may not be able to get this game anymore if you hadn't already (it was free for a limited time). The rest of the digital offerings are all pretty much 1:1 ports of the original versions (e.g. even the Wii U release of Skyward Sword isn't up-rezzed or enhanced in anyway, as far as I know).
The other question are whether you're interested in collecting/playing the Zelda spin-offs. First, definitely get Hyrule Warriors (or the new Switch version) if you at all like the story behind Zeldas. If you like the quirky-ness of Tingle, you may want to check out the Tingle spin-off RPG (English language version released in Europe). There's also a Japan-only sequel (Irozuki Tincle no Koi no Balloon Trip), as well as a Japan Club Nintendo-only Balloon Fight cross-over (Tingle no Balloon Fight DS). They can get confused because they have similar names and are Japan only, but they are very different games. There's also Crossbow Training on Wii which I would suggest getting if only to justify owning a Wii Zapper, and I would suggest printing your own custom cover (it only comes in a cardboard sleeve just like any Wii Sports pack-in copies). There's also the Satellaview games which you CAN buy "homebrew" copies of from various websites if I do believe, or you could just download a copy to either play in emulators or play on hardware via flash carts. If you're going really hardcore, there's also the very expensive Game & Watch handheld dedicated game (I think also a smaller, newer version released in Europe that's also rather expensive?) as well as a "Watch" game (this one is a digital watch, that has a Zelda game playable on it, and is different from the Game & Watch game). Finally, there's the Phillips CD-I games, but they're not really official, are crap, and WAAAAY too expensive (both the games and the consoles).
2) I'd say, look at it from a content perspective first, and aesthetic perspective second. For disk games (GameCube and later), I don't think there are any differences for Player's Choice/Nintendo Selects, so go by whichever is cheapest/easiest or whichever coverart you think looks best. For Player's Choice, there really isn't much different, but I HATE Nintendo Selects covers, so unless you don't mind them, I would avoid at all costs (literally - I'd pay 2x more for a non-Selects...). For cart, I think there may be a few differences between different versions which you may want to keep in mind if they matter to you. The biggest example is probably Ganon's blood color in OoT. Other than that, it's really only whether you want a gold/regular cart for most of the console games.