If you mean best as in most powerful, then the G4620. However, the G4560 performs nearly the same while costing a fair bit less, making it far better value for money. As far as I'm concerned, the G4560 is the only dual core Intel CPU worth buying at the moment.
There's no reason to move from a G4560 to an i3. They perform nearly the same (both are dual cores with hyperthreading, similar clock speeds) while the i3 costs a lot more. Like I said, the G4560 is the only dual core worth buying. If you want to upgrade from there, the next step is an i5. You could upgrade to any 6th/7th gen i5 from a G4560.