Twin Snakes is how I first played Metal Gear 1, it's... pretty great!
I absolutely loved Snake Eater though. And storyline wise, I don't think playing MGS1 (much less 2) helps at with understanding 3. Other way around, really. I'd explain further, but that'd be spoilery territory.
So personally, I'd recommend playing 3, then 1. Then... probably 2. It's chronologically and mechanically next after 1, and the characters are pretty interesting. Eventually. Just be prepared for things to get really, REALLY weird. I think the last third or so was really weak honestly, and made up for it in craziness.
Next would be MGS4 I guess, but I haven't had a chance to play it. It's also chronologically the end, and from what I've heard, it looks like a good end to the series. (particularly due to one showdown I've watched on youtube, heh). So I dunno but I'm holding it off for last, personally. Well, also it's absolutely PS3 exclusive, so yeah
So after that, MGS5: Back to Big Boss. Except that I'm pretty sure one should play Peace Walker and Ground Zero before 5 (Phantom Pain) if possible. It's hardly *necessary*, I didn't, but there seemed to be a lot of context I missed out on. Certain things probably didn't have the impact they were supposed to have.
Sorry for verbosity, I'm procrastinating.
3,1,2?,5,4??
Edit: I talked about 4 being last but then didn't put it last, derp
Take all this with a lot of salt, because the order is actually super flexible