If the engine is standard, the 500 brakes WILL suffice, depending of course how you drive it. Very high quality brake shoes for the 500 can be obtained from Middle Barton Garage who have had a batch of shoes made by Ferodo to the original Fiat specs. If you do fit these shoes, retain AND USE the original brake-shoe return springs.
The next move would be to move up to late 126 drum brakes---but to do this you will have to find a 126 (with a 650 engine) and transfere all the brakes, wheels (different wheel-bolt pattern to the 500) and front hub units to your car. You would end up with stronger front wheel bearings and drum brakes perfectly capable of coping with the extra performance.
The third alternative is to fit disc brakes to the front (ONLY). This is not a cheap option as they would need to be specifically for 12inch wheels, but there are a number of kits on the market. By fitting the smallest available rear wheel cylinders, you can get away with retaining the original 'single-circuit' master cylinder. Eventually it boils down to how much you want to spend, with regard to your driving style