Hills should be alot easier with the gearing you have compared to what you had before. As for the hill climbing part, there are different ways to go about it and it also depends on the hill. Here in Florida, we don't have much for hills, so changing gears while climbing is a cinch, just have to pedal hard a couple of times to get the momentum going so the chain won't jump off. But, if the hill has a steep incline, it might be best to be in the gear you want to climb in.
Congrats on the new bike!!