When you start a new game series...

Just depends really. I played maybe an hour of the first Assassin's Creed and hated it. Never bothered with the story, but 2 was an amazing game. My first Splinter Cell was Chaos Theory, though. I know the first 2 were good games themselves, but when I tried to play the first one, it annoyed me that there were certain features not available.

If the earlier games are pretty old, I have no problem looking up the story so I'm somewhat caught up.

For me it's based on a number of factors.

Like when it comes to Zelda games, I can play skyward sword and then go back to Link to the Past and still enjoy that game even though skyward sword has way more features. I guess when games in a series age well with time you can do this.

Now if I was just getting into the Metal Gear Solid series, I would for sure start from MGS just because there was way more emphasis on story than gameplay.

Typically if it's a series of games where all the games build upon each other heavily gameplay wise, for example Resistance 1 to Resistance 3 or God of War 1 to God of War 3, I play them in order or else you'll just get frustrated by the lack of features.