I am a HUGE FAN of the seires. Honestly, I play it because it twists a western story concerning the US and other nations with lots of japanese art and style (characters are extremely unique which adds a lot of value on the game).
There is Metal Gear Solid 3: Subsistence for your PS2. Then I recommend getting the HD collection for the 360 that includes Metal Gear, Metal Gear 2, Metal Gear Solid 2: Sons of Liberty, Metal Gear Solid 3: Snake Eater, and lastly Metal Gear Solid: Peace Walker.
The rest of the holes in the story you can just look at the Wikipedia about that game. One of the best things is that the story and complexity to understand it requires additional reports and opinions to look out to. The story leaves a mystery and unknown purpose of event for Snake.
The game play requires lots of stealth and patience. If you're not into taking your time in this game you might become frustrated. Also the controls will not come regularly for you and will take some time to adapt.
The first game to play is Snake Eater. Although it is deemed the 3rd Metal Gear Solid, it is the prequel to the entire series. Technically, you could probably find Metal Gear Solid 3: Snake Eater for the PS2 for around $5 on eBay or something.
Be advised, the PS2 version does have some issues and fans complained. First the frame rate issues will bug/annoy the shit out of anyone if they are looking for flawless game play. Even the 3DS version of Snake Eater has frame rate issues, but they are not extremely bad.
TL: DR
Recommended: HD collection if you got the ca$h
Must: buy Snake Eater for the PS2/rent it to try it out for yourself