Asellus - A woman run over and killed by the lord of Fascinataru, Orlouge, who is subsequently given his blood and reanimated as a "Half-Mystic". She attempts to escape his evil influence with the help of Princess White Rose, but continues to get caught up in his schemes regardless.
Blue - The most powerful sorcerer of the Magic Kingdom, tasked by the ruling council with learning all of the magic he possibly can and killing his twin brother, Rouge. A pretty collection-centric quest with a bit of plot on top.
Emelia - A woman framed for the murder of her fiancee and sent to Freedom (the ironically-named prison of this universe), she attempts to escape and discover the identity of the true killer, which in turn leads to her joining a secret agency. A fairly short, but enjoyable story.
Lute - A country kid who plays (what else) the lute, who departs his home town in search of adventure. Pretty standard, and also the shortest and most nondescript quest.
Red - A man whose father is killed when they come under attack by the criminal syndicate Black X. Red himself is severely injured and left for dead, but saved by the superhero Alkarl. He now wages a battle against Black X under the superhero identity of "Alkaiser". One of the longest quests, and also one of the most fleshed-out and generally fun.
Riki - A monster whose home, Margmel, is onset by plague and famine. He leaves his home and takes on a humanoid form in order to seek seven magical rings and save his homeland. A fairly long quest with some very challenging bosses, and quite fun besides.
T260 - A rusty, battered old robot found in a crater, who seeks to recover his lost memories and fulfill his programmed mission objective. One of the longer quests in the game, and arguably the most well-developed character in the game.
As you can see, SaGa Frontier was definitely a grand project, but unfortunately suffered from a rushed production that resulted in a lot of ideas being cut - several maps, graphics, events, a couple characters and even an entire quest were left unused or incomplete. For more info, check out the TCRF page on the game.
We're going to let's start things off with Emelia's quest. It's one of the shorter quests in the game, but it's well written and pretty enjoyable overall. I'll also give you the rundown on the game's most amazing money-making trick, Takonomics.