ashe is the easiest to play when u just started league. it is a very simple champion whose damage mostly come from her right clicks. She does not have any mechanics, and its simply point and shoot and cast some spells.
this patch is not the best for champs like her tho ( adc or champs that rely on right click damage).
annie is also another great champ. her mechanic is not complicated, she can stun, and she can burst most enemies down in one combo.
In general u want to start with simple champions so that u can learn the game. Once u get a better hang of the game, then u can start learning more mechanical champions.