Usually the noisier is just the squeaking when you brake. Reusing the shims might cause the rubbing sound, but it's hard to say for sure. The rubbing sound is most likely vibration in the brake pad as you come to a complete stop and the pads kicking off of the rotor as you start moving again.

What brand did you get?

It could be normal for those pads to make that noise. If it's stopping good, the pedal doesn't feel spongy, and the wear on the rotor and pads look uniform I think you'll be okay. As long as it doesn't make a rubbing sound while you're moving! I'd keep an eye on it just in case. Worst case you spend too much time looking at perfectly good brakes!