Pool of Radiance, Curse of the Azure Bonds, Secret of the Silver Blades, Pools of Darkness. That is the series you will bring character in to play all 4 games in a Series. Of note, the later games add classes that are not available in the earlier ones.
Good fucking luck with Pools of Darkness.
Gateway to the Savage Frontier, Treasures of the Savage Frontier will use the same party for only 2 games (BONUS: It's the FIRST cRPG to include ROMANCE!!!111!!!!11).
Champions of Krynn, Death Knights of Krynn, The Dark Queen of Krynn will take a party through 3 Series. Really fun game to play through.
Have fun, and MASSIVE INCLINE upon you.