Big metal gear fan here, prepare for what might be a bit much:

There are a couple of good startig points depending on what you as a gamer want, and I'll try to explain them without spoiling things because figuring out MGS is part of the fun (I'm quite proud that I have an encyclopedic level knowledge of this stupid series)

Metal Gear 1 (MSX) - Either grab an emulator or a copy of MGS3 remake and you can play the very first game in the series. It'd get reconned massively but playing it still gives you the info you need to understand basically all the background story. But, tbh, it's not a very fun game and if you don't want to play it having someone like me explain the story to you would work just as well

Metal Gear Solid (PSX) - The first 3D game in the series (solid) and where a lot of us started. Probably the most common starting point and I would likely recommend it as the best. Won't say too much cuz it's better to go in blind.

Metal Gear Solid 3: Snake Eater - The earliest game in the timeline, so starting here with Naked Snake (big boss) would let you see the series unfold chronologically, but you'll also have plot points from later games spoiled and explained before you get to them, ruining the effect somewhat I'd say.

MGS1 is likely the best bet. MG1 is good if you can handle what it is, worth giving it a shot at least. MGS3 is good, too, if you're more concerned than the one 5about understanding the series without needing to replay the games after beating them all so you can see how shit connected.

As for which games you need to play, some aren't canon, so just avoid: MG1&2 on the NES, Twin Snakes remake on GC, the GBA game, and Acid! The details of Portable Ops aren't canon, but the general story is, that one is up to you if you wanna play it, I think peace walker is so much better that it's a skip, personally.

Always down to answer questions or discuss MGS if you need it, shits amazing

I also recommend Metal Gear Solid 1, it's a fantastic game and it works well on PSP!