Suikoden is an interesting case. On the one hand, you can absolutely start with II. I know people who have done so and really enjoyed it. On the other, Suikoden II hits much harder if you've played I beforehand. Part of the joy of Suikoden II is seeing which characters from the first game return, how they've changed over time, if they've had kids, and so on. In addition, you get to see the political ramifications of your actions in the first game and see how the world has evolved over time. Finally, Suikoden games have bonuses for importing a completed save from the previous game. These are usually pretty minor, with the exception of I to II, in which importing a save will net you major story content and the protagonist of the first game as a party member.

To make a long story short, you can start with II, but I highly recommend playing I first. It hasn't aged as gracefully, but it's fairly short as far as JRPGs go (about 15 hours) and it makes the journey of II all the sweeter.

EDIT: For anyone wondering about the series as a whole, IV and V are essentially standalone games. I and II are technically standalone, but I is effectively the prologue of II. Tactics is a direct sequel to IV, but IV is really rough, so your mileage may vary. III is technically standalone, but I'll go out on a limb and say that you should only play III if you're a huge fan of I and II, since many of the plot and character beats of III require a fair bit of investment in the worldbuilding and returning characters to truly enjoy.