[Variol (Farseer) Elmwood]

Lets just say the game doesn't lend itself to this type of party very well. But if you're going to have Legolas he has to be a Ranger. No other class can excel in the Scouting ability which was one of his strong points. He could see what the others couldn't. Give him a bow, of any type and two daggers for melee since you can't use an arrow as a melee weapon which he used to great effect a couple of times. This is also the best choice for the mythology skill, because Legolas is old he knows the races. He should also not wear more than leather armor.
Aragorn should also be a Ranger because he is a Ranger! There are enough choices of melee weapons for him that he won't be too restricted. He can be made into a Lord late when he becomes the King, but this will have some drawbacks. The restriction to chainmail is also good since that was the most he ever wore.
Frodo and Sam are a bit tricky, but I think Rogue would be the closest. I would build their mythology and artifacts, or something and a lot of stealth besides combat since they really never were good fighters.
Gandalf would be really difficult because of his fighting abilities. I think I'd give him a few rounds as a fighter and then go to.... I guess Bishop? He really never did much magic throughout the entire book if you think about it. He never cast much in the way of healing, I guess he could cast anything. He would also have to be an elf, since you can't pick a god as a choice and he did have one of the three elven rings.
Gimli is dwarven fighter, plain and simple, with axe ability.