Where to begin playing Legend of Zelda?

Where to start is a challenging question... one that really don't have a decent answer since MOST of the Legend of Zelda titles are self-contained adventures (some titles do lend a bit from another game, but it's more of a lead-in than anything).

For an game to ease into the series, I would recommend starting with A Link to the Past (GBA / Wii SNES VC, 800 pts, Classic Console / Gamecube controller REQUIRED) as the storyline helps guide you through the game & the world map helps to point where you need to go (HOW to get there is another story).

Ocarina of Time (Wii N64 VC, 1000 pts, Classic Console / Gamecube controller REQUIRED) would be a great second choice as it's the most critically acclaimed title in the Zelda series. Playing without an N64 controller does take some time getting used, but a Gamecube controller works fairly well by comparison.

Moving on... Link's Awakening / DX (GBY / GBC) would be a good starting point on the portable side. It's somewhat blends a bit between the original Legend of Zelda in mechanics & A Link to the Past in terms of storyline (as the game points you towards you next destination). I would hold off on Oracle of Ages & Oracle of Seasons as those titles are a bit harder in terms to gameplay (& changes the second title a bit when you complete the first).

If you're ready for "NES hard" gameplay, dive into the original Legend of Zelda (GBA / Wii NES VC, 500 pts). Just be warned that the original game doesn't guide you in ANY ASPECT, so be prepared to reference at least a map on Game FAQ's (or other preferred guide sites) to provide enough assistance to stave off potential rage-quits... HOWEVER, you may enjoy the freedom of not being forced to clear levels in a particular order OR finding out the secrets to the game yourself. I will note that A Link Between Worlds (3DS) makes a return such roots by allowing you to explore the dungeons in any order you wish.

From here, you'll be able to take on The Wind Waker / HD (GCN / Wii U), Twilight Princess (GCN / Wii) & Skyward Sword (Wii) at your convenience... in addition to the other Zelda titles NOT LISTED.

Please be aware that Twilight Princess & Majora's Mask are consider the hardest Zelda titles in the series for two different reasons. Twilight Princess went towards a realistic feel, which made the game LESS FORGIVING (lesser rewards, harsher penalties) than others.

Majora's Mask (Wii VC, 1000 pts, Classic Console / Gamecube controller REQUIRED) added a critical time element as you only have 3 game days (= 72 - 144 minutes) to complete as much as you can before you have to go back to the start of that cycle. That time limit forces you to reach specific checkpoints (like defeating a major boss) within the game's time cycle to move forward. I will note that once you reach such checkpoints, you obtain a key item that allows you to bypass that area in future cycles. There's also certain tasks that can only be started at specific times within the 3-day cycle, which requires you to additionally manage your time as failing to meet or talk to a person at a specific time will force you to try again on the next cycle.

Hope this helps!

I wouldn't worry about order of anything.

The "best games" to start with would be the SNES "Link Between Worlds" and N64's "Ocarina of Time"

The new aspects of those games still carry on to current games.

After those, then you can start opening up to some of the others, such as Windwaker, Skyward Sword, and Twilight Princess.

If you go through those, and you're not tired of the series yet, then you can start getting into some of the odd-balls: the NES games, the portable games, Majora's Mask, etc.