So I just want to say because I played every game in the Metal Gear series to completion (I beat Metal Gear Solid 4 three times, Metal Gear Solid 3 twice, Metal Gear Solid Portable Ops twice, Peacewalker once, MGS2 twice, Metal Gear Solid once, and I even beat the MSX versions of Metal Gear 1 and 2), don't listen to these idiots (which includes Hideo Kojima) telling you to buy Peacewalker before you play The Phantom Pain.
The game's story is utterly incomprehensible, and worse, it's actually less significant to the plot than Portable Ops.
Whereas Peacewalker is about a minigame where you build a secret base and then something about Nicaragua, Portable Ops told you about Big Boss's defection, Ocelot's motives, the betrayal of Fox against the US gov't and Big Boss, the origins of the Grey Fox of MGS1-2 fame (also big in Metal Gear 2: Solid Snake), and the practical origins of what became Militaire sans Frontieres in Peacewalker.
They try and trick you at the start of Peacewalker into thinking that anything contained within is actually relevant to the plot by giving you a voice recording of The Boss. This is a trap. Do not believe them. Do not play this fucking game.
You will end up spending literally hours shooting Metal Gears and attaching Fulton recovery balloons to random guards to make your research progress move faster, but it is utterly without merit. The briefing tapes are utterly useless.
Even though this is ultimately superior in terms of gameplay to Portable Ops, it offers nothing in terms of backstory that you can't already glean from the rest of the series or infer within 5 minutes of listening to the briefing tapes in Ground Zeroes. What's even more, you won't discover the plot of Ground Zeroes unless you complete the secret ending mission in Peacewalker, so Ground Zeroes will probably end up spoiling it anyway (it did for me).
If you're looking for the best gameplay experience in the series, without a doubt Metal Gear Solid 3, Metal Gear Solid 4, and Ground Zeroes are the best in the series thus far. I would recommend that you skip the cutscenes in MGS4 and you should be gold.