First off: How much damage a character is able to deal depends mostly on your own skills as a player. In Lunia you deal a lot of damage by air-comboing your enemies, which results in multiplied damage output. Simple skill spamming won´t get you that far, unless you spend all your time in easy mode, but then you´ll have problems in Myth (endgame content), where comboing is highly recommended.
Since you´re new to the game I suggest to try out one of the free characters first. Sadly, Asuka is not a free character, so in order to play her you must get her license by clearing a ridicolously hard quest or by purchasing her in the cash shop for $9.
Asuka is pretty easy to control and it´s also easy to combo with her, so she´s not a bad choice for beginners. However her damage output will be below average, because she´s not balanced yet, and also has problems with dealing lots of damage on uncomboable enemies.
Tia is probably the hardest but also one of the more rewarding characters to use. With some of her skills and buffs you´re able to kill bosses within seconds but comboing efficiently with her is really hard. If you want to use her, you have to spend a lot of time in the Practice Field.
If you want a character, who can deal lots of damage by simple skill spamming, try out Arta. She´s probably the most straightforward and easiest to use character, because you don´t even need to know how to combo with her. Use a skill and watch the enemies die -well, most of the time :P At Myth you won´t be able to kill as fast as in normal stages anymore, but that´s not really a problem. Just team up with other players and let them lift the monsters in the air, so you get a high air-multiplier automatically by hitting them with skills.
Arta´s disadvantage is her pretty long casting time on some of her skills, so keep your distance if you want to use one.