I would recommend the first 5 games in the order they were released so one can properly evaluate the evolution of the series.
1. LoZ so a new player has a baseline from which to judge the series. i believe origins of anything, whether it be words and their definitions or entertainment series, to be extremely important in defining what a thing so that we can judge whether any alterations or additions to that thing helped or hurt. Plus, like you said, it's quite different from the rest of the series. I personally think Nintendo needs to go back to square one with this series and bring back tougher combat, gloomy dungeons without the themed gimmicks and puzzles, and a faster pace, but with improvements to environmental variety, boss battles, dungeon layout, and item selection. Call it New Legend of Zelda and watch it be a surprise hit akin to NSMB.
2. Adventure of Link. Message board revisionism abounds with this game. But it remained in top 10 NES lists even past the launch of the SNES - not quite the black sheep people who probably weren't even alive then claim. Some of the best side-scrolling sword combat of the day, and it's an early example of how the series can go in a different direction while maintaining the original spirit. It does have questionable design decisions, but like its predecessor. its uniqueness within the series makes it a must play.
3. A Link to the Past - Overrated to me, but still a near flawless game in terms of polish and content. Expands the series by offering more visual variety, more geographical variety, more fleshed out NPC interaction, more narrative thrust. The series would become more whimsical and fairy tale-like from this point on. A must play just because of the extreme high quality and, being a turning point in the series, for comparison to what came before and after.
4. Link's Awakening - A better version of Link to the Past, imo. Not as groundbreaking for the series, but so well crafted. And somehow recaptures the spirit of the original game while maintaining the additions of ALTTP.
5. Ocarina of Time. Huge game for the series and 3D games in general. Its structure would define LoZ going forward, sometimes to a fault. Due to this, it's the only essential 3D game in the series. Introduced Z targeting. Made themed dungeons the status quo.. Established the type of puzzles the series is now known for. Introduced mounted/piloted transport (as far as I'm aware). It's just one of the most significant releases in the series and in video games in general.
Maybe I should have made my own blog on this, but that's my take on the essential games.