(UPDATED) The Phantom Pain actually might be Metal Gear Solid 5

[retrolinkx]

Snake Eater (MGS3) (PS2/VITA/XBOX/PS3)
Portable Ops (MGPO (PSP))
Peace Walker (MGPW (PSP/XBOX/PS3))
Ground Zeroes
Metal Gear (MG (MSX/MGS3S))
Solid Snake (MG SS (MSX/MGS3S))
Metal Gear Solid (The Twin Snakes) (MGS/MGS:TTS (PS1/GC)
Sons of Liberty (MGS2 (PS2/VITA/XBOX/PS3)
Guns of the Patriots (MGS4 (PS3)
Revengeance (MGSR (XBOX, PS3)

Chronological order right there.

But for the best experience it's better to play it in release order, and only the Solid series, since the other two aren't that important to the storyline, as there are some links in Solid 1, but that's it.

So the best order to play it would be this below, unless you want to play the MSX versions.

MGS
MGS2
MGS3
MGSPW
MGS4

Also, never play 4 first, it'll literally ruin everything for you, since MGS4 was Kojima's way of trying to finish up the story.