So the only Metal Gear game I've ever actually played was the 1998 Metal Gear Solid for the PS1 when I was a kid. I've not played a single other game in the series since.
Which ones would you recommend? Would it be better to play them in chronological order to get the full overarching story, or do they work ok independent of one another?
If you want to play them definitely play them in release order. MGS1-5, Ground Zeroes and Peace Walker are the must play ones, but Metal Gear Rising is just too fun to skip.
I'd also advise you that you need a whole lot of patience for these games. A significant amount of playtime is spent not actually on gameplay or even on cutscenes, but on codex conversations, which feel genuinely archaic in their worse-than-any-visual-novel presentation. Like I've tried replaying MGS3 recently and I can't believe that there's no way to skip through the voicelines without skipping all of them. In any visual novel you can skip the currently playing voice line and you'll immediately hear the next one, but in a MGS codec call you either listen to every single voice line in full, as as soon as you skip through one you'll just get the text for the next one without the voice acting, making the entire conversation entirely silent (or at least it's this way in MGS3, unless I'm really misremembering things).
Like I've replayed Disco Elysium like three times, which is a game with so much more text than any MGS game, but I've not had the patience to play through any of the MGS games a second time, just because the codec calls require the patience of a saint from you.