I always play them in release order because the older mechanics can be a bit janky to go back to.

The first 3 are a must, peace walker is also a good addition and is like a bite sized version of 3. 4 is 4, i personally really like it but its divisive and then 5 i never finished cos its too long. Then there's portable ops and acid which are worth playing if you really like the series. Metal gear rising is also a must and doesn't particularly need the context of any of the other games to be enjoyable, PC version has some odd issues so i picked xbox backwards compat to play that one.

Deffo do the first 3. Duckstation is a solid option for the first game, much better than the shitty konami release.

2 and 3 I'd suggest the HD edition on the xbox 360. If you don't have the disk and series x then you should be able to emulate it i think i haven't tried in a while. I say this because emulating the ps3 or ps2 versions of these games requires you to have pressure sensitive buttons for certain actions. The xbox version however you click the left stick to say cancel a shot for example. If you're feeling adventurous the 3ds version of mgs3 is fun on real hardware, framerate is atrocious though but it has crouch walk and migraine inducing 3d :D

The recent versions konami released are also the xbox hd edition but i think they also just broke some shit cos konami. PC version has mods to fix it.

Peace walker you can either do the hd version or emulate the psp version. The HD one has dual analogue stick support.

4 i don't think is easy to emulate atm. It requires a specific fork of rpcs3 and performance is spotty and may require some sixaxis inputs but worth a try. Otherwise you need a real ps3 to play.