Well, there's no real mage/magic classes in the game. Loremaster is closest you get to that. Its a pet class with some interesting debuff/melee/ranged attacks plus CC. Hunters unlike WoW don't have pets, they rely on all out nuking like a mage or destro Warlock would, plus traps and CC which is more useful when grouped.
Melee classes are a big thing in Lotro. There is 3 melee fighter classes, Guardians are obviously tanks, Champions are high damage melee with AoE attacks. And Captains play as good group buffers and utility, they are also a pet class but the pets are buffers rather than fighters/tanks. Then you got Burgulars which are similiar to Rogues but can be very useful in groups with some unique abilities. Minstrel, is a Bard/Healer class.
For soloing, any will do but Hunters and Champions would be the most straightforward and fastest. Minstrels too, but they are slower at leveling. The other classes can be a bit more tactical, although my first character was a Loremaster and enjoyed it immensely....but I do have a thing for pet classes.
As for race, it really doesn't matter that much overall, although some are restricted in what class you play. My advice is just choose a class/race combo you fancy.
