There is no best characher to start with, i hate that question.. it depends how good u play, how good u buy against ur enemy in ur lane!
1. so basically the games is 3 lanes, top/mid and bottom.
at bottom there is attack damage carry and a support that supports the attack dmg carry! (atk damage is usually a charachater that is AttackDamage and Has Range, support helps him to kill and farm creeps.
2. mid is 1 guy usually AbilityPower based charachter but it can also be a attackdmg(ad), mid is ganking(helping bot or top killing someone and make em cash!
3. top laner is usually a strong tanked AD, but as mid it can be AP.(abilitypower)
start with an easy charachter like.. hmm , maybe TEEMO, he is pretty easy and EXTREMLY fun to play if first time, go toplane or mid with him and build alot of attack speed, kill creeps and get cash to buy good items.
gl!