How do I to choose a new light fixture for the bathroom?
Two factors affect what light bulbs you can place. The first is the branch circuit load, which  is the total amperage (watts / volts * safety margin). That must be less than the rating of the circuit breaker. The safety margin is 1.25, which gives you a loading of 80% of the breaker's capacity. This is to account for some resistance loss in the wire, initial startup surge, etc. See also How do you plan capacity for electrical circuits? and the National Electric Code if you're in the US. (NEC basic rules and design)

The second factor which will matter less since you're replacing the fixture is the heat loading of the fixture. When you see a fixture that has a wattage rating for a bulb on it, that rating is typically far lower than what the power cord is capable of handling. The rating is based on the amount of heat that would be generated by an incandescent bulb of that wattage. Overloading that is a fire hazard.