MGS1
MGS2
MGS3
MGS4
MGS PEACE WALKER
DON'T PLAY GUROUND ZEROS!! IT'S A SCAM!

I would play them in timeline order which is...

MGS3
MGS PO (but its questionable if its canon)
MGS PW
MGSV GS
MGS PW (hasnt released yet)
MG
MG2 SS (both included in mgs3)
MGS
MGS2
MGS4
MGR R (you dont need to play MGR since its a spin off and not considered canon....also it kinda sucks lol)

However you could play them upon release. That's what I did...well because I had to wait year after year for them to release haha. The only games i didnt play but played later were the original two MG games. Back on topic it might be easier to play in order rather then going back and forth between the different games because of the evolution of the games from story to game play. 

Hope that helps and enjoy a great series.

Twin Snakes was not deleoped by Konami and adulterated the original in some silly ways. Don't bother with it. The original is still perfectly playable and great fun, apart from two sequences that are a bit awkward control wise. You'll be fine.

Hideo Kojima was supervising the development of Twin Snakes though...

'Supervising'. Lol. 

And Konami themselves don't care for it:

That was a remake made by Silicon Knights. We supervised it but we didn’t create it directly and we wanted to make sure that everything in the HD Collection was canon. Everything that goes into there is something created directly by Kojima Productions and Kojima himself. So that is the reason why Twin Snakes was not included in HD Collection.

Yes, nothing would have gotten into that game unless Kojima said yes to it...

Hmm this is a hard one. I grew up and first played the original so id always recommend that one. However to a new comer, playing TS might be easier and more enjoyable because you still get the same story ontop of better voice acting.

Just kinda ignore the silly over the top stuff in the cutscenes even for mgs standards. Another con about TS is the music...wasnt really a fan of the replaced score.

You should play the one you prefer. I just brought it up because the stuff added wasnt added without Kojimas approval:)

I consider the voice acting and cutscenes as inferior. If you don't have a problem with PS1 grapphics I'd recommend the original every time.

This argument mostly boils down to which version you played first back in the day. But the comment from Konami about sticking with the games directed by Kojima himself seems pretty reasonable to me.

That is true. I recommend and prefer the original in every way but ive known people that couldnt get into it because they didnt grow up with it or because its old.

As for the voice acting im only saying that because the acting itself is better preformed and consistant with mgs4 even though I also prefer the original.

I dont think TS is bad at all so thays why I give people the option.