Bring it to a NEW shop or do the brakes yourself. It's about the easiest repair you can do. Basic tools are needed and tons of videos on YouTube walk you through the process. And the cost will be a lot less than bringing it to a shop - maybe as low as $200 for the front rotors and pads and secondary parts you will need. (The cost will vary greatly depending upon the specific vehicle)

Also while the front brakes do do most of the braking, so they will wear out before the rear brakes, don't forget that the rears will need servicing eventually.

Squeaking usually comes from not lubricating the pads when you put them in. Or it can come from not lubing the caliper components.

Shaking usually comes from rotors that have warped from heat. And braking your car produces a LOT of heat. You mentioned that the rotors were sanded down. I hope they weren't sanded down. They should have been turned down on a lathe. That will give you a smooth even surface for the pads to grab onto. But the problem with turning down the rotors is that they are now thinner, and thinner materials tend to warp. Usually it isn't worth turning down rotors. The mechanic might charge you about $50 to turn them down, but new rotors would probably cost only about $100, so you are far better off replacing the rotors instead of turning them down.

Sometimes shaking comes from the pad material leaving small bits and pieces of itself onto a hot rotor. That happens when the pads haven't been "bedded-in" properly. I'm not going to explain that - there are plenty of videos that explain bedding-in brake pads you can watch.