You should play some of the other games in the series, but stick to the 2D ones. I have a feeling you wouldn't like the 3D ones as much. Especially not Twilight Princess or Skyward Sword. All the 3D titles give you a companion who is constantly telling you what to do, and from what I can tell you don't enjoy that. But you might enjoy A Link to the Past (SNES) or Oracle of Seasons (GBC). They play like the original but with better graphics, more interesting items, better level design, and new mechanics to keep thinks interesting. OOS is a bit more railroaded than the earlier installments, but I love the season-changing mechanic. Also, it has a sister game called Oracle of Ages, but I wouldn't recommend it as highly- the 'gimmick' for that game is time travel, which is not only incredibly overused but it doesn't even pull it off very well.
EDIT: as far as the 3D titles go, actually, you might like Wind Waker. Your companion in that game is a boat, so he's not really able to follow you around everywhere. He pretty much just drops you on an island, tells you to do something and it's up to you to figure out how to do it. Also the overworld is HUGE, despite being mostly water with islands scattered about. The ocean is actually pretty clever, as it puts enough space between areas so that each island is able to load as you are approaching it. But it's a Gamecube title, so you would need a Gamecube or Wii to play it... IDK if you have either of those.