Lots of people will tell you The Twin Snakes is garbage and to only ever play the original, but I never understood that narrative and I'd say to take those opinions with a grain of salt. The original is a masterpiece, of course, but The Twin Snakes absolutely does not ruin it and plays + looks better to boot.
That said, some of the voice actors were replaced with inferior actors in The Twin Snakes (though not always; there's at least one actor I would say is actually an improvement over the original, but I'm biased in this case) and there are people who believe that the over-the-top quality The Twin Snakes adds to some of its cutscenes ruins the vibe. I disagree with those people, but what can you do? Still, it's a fair criticism.
TL;DR - There is no wrong way to play MGS and it's an absolute classic no matter which way you go about it. The original is a masterpiece that holds up today, and The Twin Snakes is a really good remake of that masterpiece with a few divisive changes. You can't go wrong either way, though.