The main thing is don't try to pick lenses on your own from the internet and don't just grab whatever comes first. You need a consultation with an ophthalmologist who'll fit the curvature and diameter specifically to your cornea. Poorly fitted lenses will fall out more often than they should and cause discomfort.
For sports, look for lenses with increased moisture content - they hold moisture better and shift less during active movement and sweating. There are special sports models with high oxygen permeability that let your eyes breathe during exertion. Ask your ophthalmologist to recommend something along those lines. Proper fit is also important - the lens shouldn't be too tight or too loose.
Practical tips: before training, make sure your lenses are well hydrated, bring some eye drops with you. If you're still worried about losing them, ask your doctor about daily disposable lenses - they're safer in terms of adaptation. And yeah, even with lenses some people wear protective glasses for combat sports, so it's not a problem. The main thing is to get used to them during training before actual fights.