You jumped in way too late. I'd recommend picking up
Metal Gear Solid: The Legacy Collection. It has all the games that matter to the story. Play them in this order.
- Snake Eater
- Peace Walker
- Metal Gear (on Snake Eater Disc)
- Metal Gear 2 (on Snake Eater Disc)
- Metal Gear Solid
- Metal Gear Solid 2
- Metal Gear Solid 4
- Metal Gear Rising: Revengance
That'll give you the entire story thus far (minus the Mobile Ops stuff, which isn't important anyway). If you like those, pick up Ground Zeros (which is between Peace Walker and Metal Gear Solid 5), then pick up The Phantom Pain if you dig THAT.