The Hero is a descendant of Maxim from Lufia 2. He learns mainly healing spells and is a very effective fighter. His fighting power is only matched by Aguro. The Hero is the only character that can use the Dual Blade.
Lufia came to Alekia long ago when the Hero was still young. She has no relatives and lives with Rome, the Innkeeper. Her speciality is in magic and will become very proficient in it later in the game. Lufia doesn't recall much about her past, but there seems to be more to her than it seems... Lufia will join you when you go to Sheran after returning to Alekia.
Aguro is the equivalent to Guy from Lufia 2. He is purely a physical attacker with no magical capabilities. Aguro will join you in Treck during the fight with the Demon Lords.
Jerin is a Half-Elf that serves as a guide for the Lost Forest. She is a bit of a weak phyisical attacker, but she is a rather strong magic-user. She is also the only character that can use Bows which attack all enemies. Jerin also has very high Agility allowing her to attack quickly in battle. You first meet Jerin when you rescue her from the Dais Tower, and she joins you when you try to traverse the Lost Forest.