if it's an epic tale, involving multiple characters: RPG
I'd prefer to see a battle system similar to Secret of Mana/Legend of Zelda.. but I do love the Tales Of... series battle engines (if you've never played them I suggest Tales of Destiny 2 (AKA Tales of Eternia) and Tales of Symphonia)
If it's the same, but with one central character, Adventure (Top down is usually good for this, but it can also be achieved succesfully with platform, if you design the levels right. I.e dont use super-short levels, constant switching of scenery tends to detract from the story)
you could also do a Turn based RPG if you want a more strategic feel to your game (think FF10 battle system, where you know the order of attack, that way you can plan ahead instead of just hacking and slashing)
As for creating custom movements, logic dictates you should use a solid object with same dimensions as your character to do all movements/collisions etc, and just have your character at (0,0) relative to it, that way animations won't interfere with movement collisions and whatnots.