What brand should I purchase to replace the brakes

ABS is short for anti-lock braking system. This is a separate system from your hydraulic brakes.
The abs light means the system has a problem and it is disabled until you fix it. The regular brakes still work as you know.
Someone needs to scan the computer for ABS trouble codes and go from there.

Make sure you fix them . This could make other break easyly and come off, To fix the easyest wat you need a ez-out and a reversable drill, Go slow and it will come rt. out. Have to remove the axle to get to it. If on front. if on back can do easyer. A tire shop might charge you $10 to replace if you go get the studs. Good luck.

Sounds like you need a brake job. I would replace the front pads and front rotors and that should take care of the problem.

Make sure the system is bled on all 4 wheels.

And, that the front end parts are all tight (tie rod ends, lower ball joints, etc.)

try using a hammer and bang on the lugnuts(put them back on not tight)also spray wd-40 and let it soak becareful wear eye protection.

Did you turn the rotors? Drivers that drive fast, brake hard and hold the pedal down hard after stopping will warp these small rotors.

If they look like a smaller version of your front brakes where you can see the disc (should be shiny on the side of the disc where the pad touches the rotor) then you have disk brakes.

If it's all black, or all kinda of rusted looking and all you see is a "cap" over everything behind the rim, then it'll be a drum...

95% of the zx3's have drums
only 5% of zx3's had discs. The ones that have disc brakes, also came with traction control as part of the package.

if rotors were turned then it is just grooves in rotor

Sounds like the pads are worn out and are grinding on the rotors. You will likely have to replace the pads and rotors.

did you have them change the rotors too ? even brand new ones out of the box often require turning (machining). replace the pads and rotors and go easy on the brakes for the first little while