The DS games really, really suck. Seeing as you're going legit, that means there wouldn't even be a way for you to remove the ridiculously unnecessary touch screen control scheme. I vote 100% avoid on those titles. I suppose if you really wanted to, you could play one of them. They're such parallel experiences though in pretty much every way that playing both is both redundant and likely a form of torture in certain countries.
Twilight Princess: This is a good game. I had tons of fun with it when I was younger, and it is certainly a darker game largely due to the darker and more serious art style augmenting the overall tone. The dungeons are interesting, and the swordplay is some of the best in the entire series due to the moves you can learn throughout if you opt to hunt them down. This is definitely a highly recommended one, although, the Gamecube version is superior to the Wii version (the Wii version is a port), so if you have a choice of either one, definitely go Gamecube.
Skyward Sword: This game gets a resounding "meh" from me. The game is really clever and interesting at first, but everything special about it quickly becomes annoying. The motion controls are inconvenient and prove that unless you are physically there swinging the sword, the act of acting like your swinging a sword just becomes boring. As well, the experience dispenses with an over world that would at least give the impression that the game isn't ridiculously linear. Between a stunning lack of actual exploration, uninspired dungeons, a relatively empty sky, and gimmicky controls, this game that received so much praise when it came out turned out to be a turd masquerading as a diamond.
Majora's Mask: This one is definitely a bit of an oddball. Now, I recently played and completely 100%'d the 3DS version of this, and I did have a lot of fun with the game. I felt that all of the changes made this into the best version of the game, disputed only by those that didn't quite get the nostalgia feeling they wanted having played the N64 version. The thing is, this one only has four main dungeons which may throw some people off, and is largely focused on side questing. For the most part, you don't need to do the majority of the side questing to beat the game. There would certainly be inconveniences, such as if you only had two bottles by the third area, or only six hearts by the time you were facing the boss in the second area, but these can be worked with if a player is dedicated enough. Other than that, you have to get used to a lot of time management, and you may even find yourself resorting to a guide to figure out how to manage some of the trickier and far less obvious side quests. The improved notebook in this version of the game makes it a lot easier to side quest than in the last, as combined with the hints you can get, most stuff is fairly easy to solve without any aid. The one exception I can think of is trying to do the lengthiest and most involved side quest that actually has two outcomes. Anyways, back on point, this game is one you have to experience to decide how you feel about it. I spent about as long on it as any other Zelda game with doing all of the side questing, but it also has the potential to be a very short experience. Keep that in mind with the $40 price tag on this version of the game.
Minish Cap: This is the GBA Zelda game, and it certainly holds its own. It plays much like the older Zelda games such as A Link to the Past, but it isn't as punishing which makes it a better introduction to the 2D Zelda titles than most of them. It is still a reasonably long adventure despite being tailored to a handheld over a decade old, and once I really sat down and gave the game a go, it managed to rank among some of my favorite Zelda titles.
A Link to the Past: Considered to be one of the best Zelda games of all time, I really don't recommend it if you aren't used to the difficulty of older games. This game will not hold your hand, and it is crushingly difficult compared to the 3D Zelda titles. With that said, once you spend a little time with it, you get used to the game and will become more able. Even then, I have to admit that I haven't beaten this one. I reached the final dungeon and just couldn't get to the final boss. I tried and tried but I simply couldn't safely navigate the final dungeon. Maybe I just suck at the game, and I'm fully willing to accept that. At the same time, the rest of what I said holds true in that as far as 2D Zelda experiences go, this has the potential to be the most fun and one of the most difficult except perhaps for Zelda 2 which is an entirely different beast.
Oracle of Seasons/Ages: A two game set with two Zelda adventures focused around different aspects of the Zelda experience. These came out for the GBC, but to this day, they remain some of the best handheld Zelda and some top tier 2D Zelda. It doesn't really matter much which you choose to play first, but they are both part of one complete experience, so they are generally played back to back as if they were a single game. If you try and like Minish Cap, odds are that these games will be up your alley despite obviously being older.
Link's Awakening: The oldest of the handheld Zelda games with the DX version for color, this is still a pretty good experience. Obviously it is 2D, and at times it can be a tiny bit confusing as it doesn't direct you quite as well as Zelda titles from the SNES era forward. It has aged relatively well and still holds up as an enjoyable experience to new and old gamers alike. It may be a little hard to get into since it does have an older feel to it, a bit of a feeling of age that can't really be escaped, but it's still a lot of fun.
That about covers my experience with Zelda games. Seeing as you like the 3D Zelda games, I recommend Twilight Princess next. If you want a change of pace and are willing to try 2D Zelda, I recommend starting with Minish Cap since it is probably the least punishing while still being fun of the various 2D Zelda experiences. If you happen to enjoy Minish Cap, then I say just take the rest in whatever order you see fit. I can't comment on the rest of the Zelda games out there, as either I haven't played them, or you already played them (WW and OoT).