As a die-hard MGS fan who loves seeing newbies discover the series, I love this question. I've read so many responses to it in various places, and here's the critical thing:
Where you start depends entirely on your degree of tolerance for outdated game styles, and how quickly you get frustrated by old-school difficulty and antiquated controls.
If you're a (Big) boss who can handle anything thrown at you, start with Metal Gear, the very original, and play in release order: MG, MG2, MGS1, MGS2, MGS3, MGSPO (optional!), MGS4, MGSPW, MGS5GZ. Playing the two 8-bit games will give you some more appreciation for the events of MGS1. However, they are extremely frustrating and unwieldily, and the use of a walkthrough is virtually mandatory. If you're anything less than completely devoted, they could turn you off of the series. These games can be found as bonus content on MGS3: Subsistence, and in the HD Collection.
If you're not quite up for that, but still want the best overall experience, start with Metal Gear Solid 1. It's regarded, for good reason, as one of the best and most important games of all time. It's the game that made the series. (I personally don't recommend the Twin Snakes version: while the graphics are better, a number of the changes really ruin the feel of the game.) The controls are still very, very old-school: you must read a manual; you won't get one of those modern tutorial levels that walk you through everything. But the game is still very playable and holds up well. You'd then play MGS1, MGS2, MGS3, MGSPO (optional!), MGS4, MGSPW, MGS5GZ.
If you get frustrated very easily, and are a child of the modern era of gaming, expecting ultra-intuitive controls and top-of-the-line graphics, I guess you wouldn't want to start earlier than MGS3. Even MGS3 has an extremely convoluted control scheme, but it's much easier than the first two games. The Subsistence version has a free-roaming camera, too. And it's by far the best MGS game. You'd miss out on a lot of what you need to understand MGS4, but it'd still be playable at least. And, if you like the series, you could go back later and play the first two MGS games, but a lot of their stories will have been spoiled for you.
TL;DR: The best way to play them is in release order, starting from as early as you can possibly handle it. Playing chronologically is a mistake for the same reason you don't watch the segments of, say, Pulp Fiction in chronological order.