I prefer a timeline approach.
Metroid Zero Mission is the first one you should play. Chronologically, it's the first in the series, and it also has the best controls and is the best introduction to the series IMO.
The Prime series should be next. 1, Hunters, 2, 3 (has a true ending that needs to be unlocked when you 100% the game), Federation Force, in that order. Hunters is a bit disconnected from the other Prime games (it's also made by different developers and is regarded to be inferior to main 2 Primes), but one of the characters in it is looking like he'll be VERY important in Metroid Prime 4's plot. Federation Force's ending supports this even more, though I advise not playing Federation Force with the expectation of a true Metroid experience, since unfortunately it's not much like that, but the quick ending scene is very crucial to Metroid Prime 4's plot from the looks of things. If anything, I recommend looking into the game's gameplay to see if it interests you, otherwise I'd skip it and watch the ending on YouTube (it's the only thing that matters in the Prime plot in the grand scheme of things).
Next in the timeline is Metroid 2: Return of Samus, but this game is extremely dated, is low on exploration, and not super fun to play (unless you're looking for a challenge due to the limitations of the system, and not game design. It's not even in color!), so I'd advise to either wait for the 3DS remake (I'm sure you have enough to play until it releases ;) ), or you could play AM2R, a fan Metroid 2 remake that's extremely true to the series' core, and plays very much like Zero Mission. The only thing to note is that it's 2D Metroid for the pros, even the Easy difficulty needs a good bit of effort.
Super Metroid is next. This is regarded by most fans to be the ultimate 2D Metroid experience, though I honestly prefer Zero Mission and AM2R due to their tighter controls. It has very expansive exploring, and will put your skills to the test.
Other M is next in the timeline, but it's often criticized as you can tell. I think the game had amazing potential gameplay wise, but a lot of it is untrue to the series, but in a different way than the other black sheep of the franchise. It more has to do with Samus' characterization, but I don't want to get into it. I recommend trying it out if you got a copy nearby, but otherwise you're not missing out much, since the relevant plot details are mostly explained in Fusion.
Fusion is last in the timeline, and has been so for 15 years. It's my favorite in the series, and it plays similarly to Zero Mission. This game blends a somewhat more contrained approach to the exploration theme of the series, but it's still open enough to be enjoyable to series veterans. It also blends a good bit of story, which is why I really want a sequel T-T
For what it's worth, I'll mention Prime Pinball. It's a retelling of the original Prime in pinball format, make of that what you will :P
Hope this helps! I know I didn't include just the mainline ones, but I couldn't help it :P
If you want to play the least as possible, Zero Mission, Prime 1-3, Super Metroid and Fusion are the ones to play. They're the ones I played before I got hardcore into the series, and they're the ones I'd recommend to play to newcomers.
