1999 Buick Century weird noise from making a stop

If it is the brakes, it sounds like one or both of them are sticking. Be sure that the calipers slid freely on the caliper pins -- use break caliper grease if needed. Your pads may not be securely installed in the caliper itself. Sometimes you need to put some brake pad glue (the red or blue stuff) on the back of the pads.
It may not be the brake at all. It could be a C/V Joint.

I don't think that the noise is from the C/V joint. if there is problem in C/V joint, when I make a turn, I will hear some noise. But now,I did not hear any noise when I make right or left turn. When I change brake disc, I did not change the caliper pin, what function of the caliper pin? if it is not working well, what problem I will see?

The the pads will be unevenly worn. The caliper slides on these pins or it slides on the caliper bolt to apply the brake. Usually all that needs to be done (if this is the problem) is to clean the old pins - or bolt - and apply some brake caliper grease. Your pads may also be rattling around as I stated.

it would be the lower control arm bushing problem, because the noise is actually right under the brake pedal, not from the wheel. How do u think?

the noise is gone on the rainy day, but on a sunny day, the noise is louder and more frequent.