Electric vehicles (EVs) are merging as a feasible alternative to existing gasoline-based vehicles to mitigate climate change and greenhouse gas emission. As the number of EVs is increasing, uncoordinated large-scale EV charging behaviors may lead to power grid instability, extra electricity fee and cost unfairness among EV owners. In this paper, we propose a large-scale EV charging coordination framework that enhances costeffectiveness, cost fairness and target state-of-charge (SoC) level satisfaction. A simple and effective scheduling algorithm, called low-price pursuit algorithm (LPPA), is proposed to minimize the charging costs by considering three-level time-of-use (TOU) periods. Under low peak power constraints, LPPA may lead to challenges, such as EVs not being fully charged or overcharged at high-priced periods. To address these challenges, a novel selective extra charging algorithm (SECA) is proposed to identify problematic EVs through future demand forecasting and simulations, providing additional charging to ensure SoC satisfaction as well as costeffectiveness. By dynamically incorporating LPPA and SECA, the proposed framework achieves the balance between cost-effectiveness and SoC satisfaction. In addition, we evaluate the fairness of charging costs for each EV by introducing individual cost gains as a performance measure. Simulation results show that the proposed framework achieves better performance than existing schemes across various scenarios, including TOU pricings, charging speeds and EV's battery capacities.