My brake pads are fine, I believe, but when I'm at a stop and I'm (for exampel adjusting my foot that is sitting on the brake pedal, things start "creaking" under the car. I suppose I could record a clip of it later but what would I need to oil or clean to get rid of that?

 

With the car sitting still and on the level, depress the brake pedal and listen. It may just be the calipers sliding on the pins as they are designed to do. You can remove the wheels and gain access to those pins. Remove each one and apply a bit of lube. That may help.

Also, sometimes, there is a bit of noise just from the fact that the pads and brake caliper pistons are moving.....