Canon info.

Are you feeling directionless? Interested in a bossy magic crystal tethering you to the universe's destiny? Has it been a while since your childhood best friend betrayed you? Have you ever thought, "really, what this war needs is more talking ducks?" Well, friend, do I have the JRPG series for you.
Suikoden is a defunct series made by the alleged gaming studio known as Konami. They share a setting and some characters and are otherwise connected by themes of politics, war, fate, sentient magical crystals, and questionable localization choices. It is extremely loosely based around the classic Chinese novel Water Margin.
Each game takes tells a complete story, so you don't need to worry about playing them in order, but if you're curious, here's how this goes, from the first game chronologically to the last:
Nash Appears, technically
In my opionon, the best order to play the games is in numerical order. If you're just going to play one game, I'd suggest Suikoden III or Suikoden V. (This may be an #unpopular opinion.)
The Gaidens
Nash is the protagonist of the two Suikogaiden games, which take place during and after the events of Suikoden II and lay some of the groundwork for Suikoden III. These are mostly visual novel side-stories for fans of other games, and they were only released in Japan. However, in 2013 (!) a group of fans released a full English patch, so now you can play both with an emulator. This is mostly just a PSA if you haven't thought of Suikoden since 2009 or so, you know, like a normal person.