I just started working through these myself a month ago or so, somehow never got around to them after all these years until now.
I know I shouldn't give Konami money for these but I'm a lazy asshole who just wanted them all in one place on Steam, easy access. Master Collection versions are fine, but there are some mods out there to fix up a bit of the jank (MGSHDFix and MGSM2Fix mostly).
I was told to go mostly in release order, and that worked well enough. Could start with MGS or the MSX classics if you want to go that far back (those also fit in nicely right after Peacewalker).
I will say that playing release order made PW feel really weird, especially since 4 feels much more modern than it actually is while PW is very clearly a handheld game, but by the midway point it legitimately became my favorite so far.
Narratively I took so long to get around to these for a similar reason, just the military theme was offputting, but alongside the camp/pulp aesthetics they're filled with, they're very anti-military and anti-nationalism. But still gotta remember the earlier ones especially are products of the times, and Kojima's never been able to write women characters.