While sports leggings or sweat pants can suffice, they've got nothing on the proper martial arts uniform. How do you know you're doing the kicks properly, if you can't hear the snap of uniform hems?
For casual training, you can wear any loose, comfortable clothing that won't get in the way of maneuvers. Make sure you cover your elbows and knees, to protect from the mat.
Unless you've chosen Muay thai, full-length pants are safer than baggy shorts! Most martial arts have flexibility training and plenty of high kicks. If you want to wear shorts, wear leggings underneath.
Proper training and sparring require a martial arts uniform in Australia. Uniforms are comfortable and protective, without being restrictive. Sports like judo specifically need a uniform for grappling moves.
You can wear a shirt under your uniform, if you prefer. There is a specific way to tie the martial arts belt and fold the uniform, which you can learn in class or from a video online.