I've got a bathroom that has a single 75 watt bulb light fixture. It's wall mounted. Unfortunately, it's old and there isn't enough light. I'd like to replace it with a sconce that has 2 or 3 bulbs. How do I determine what type of sconce to get? How many watts? How do I know if the circuit will be overloaded? I'm going to hire an electrician to do the work, but I want to buy the right fixture for him to install. The home was built in the '60s.
Put simply, in a residential structure no light fixture you can buy in a commercial big box outlet is going to pose a problem.
Most residential circuits are 15A - some are 20A and some are 10A.
A 100W bulb on a 110V system uses just under 1A, so your light fixture would need to have a minimum of ten 100W bulbs to approach the threshhold for your house's circuits.
Plus you can get CFL bulbs which produce the same amount of light at a fraction of the wattage.
So - get what you like.
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.
If you replace the bulbs with LEDs or CFLs, the electric draw and heat output concerns both become moot since those bulbs use only a fraction of the electricity and put out a fraction of the heat.
I would strongly urge you to consider LED bulbs–the price premium is insignificant compared to the cost of the fixture, the electrician, and the lifetime electricity usage of the light. In return for a modest upfront investment you will be repaid with a cool and efficient bulb that never needs to be replaced. Today's LED bulbs come in a range of colors and brightnesses, are dimmable, and last for many decades. Big box stores near me have several great bulbs in the $10-$20 range.
If your house was wired properly, one fixture will not overload the circuit. The real question is how much light is enough light? We know 75w in your existing fixture is not enough. Fixtures vary greatly in how efficiently they put out light. One fixture will make a 100w bulb put out plenty of light, another may need 150w for the same amount of light. Fixtures are rated with a coefficient of utilization that is a measurement of this property, but finding this rating in the product specifications can be difficult.
Another factor is where the light is projected. Some fixtures spread it all around. Some only downwards or upwards or both. The color of the room's walls an ceiling affect light utilization as well. If you can gather all the information, there's scientific ways to quantify the actual lighting level. But just being aware of these factors will probably be enough.
You also don't want too much light, it not only wastes energy, but can be uncomfortable when your eyes aren't adapted to higher light levels. Try to determine how much incandescent wattage you need. You could bring in some cheap clamp on lamp fixtures and bulbs of various wattages to establish a proper lighting level. Be sure whatever fixture you get can handle this wattage, many are surprisingly limited.
If you are going to convert to CFL or LED lamps, do not go by the equivalent wattage on the label. A 21w CFL is not similar to a 100w incandescent. More like 70w IMO. I've no idea about LED conversion, I haven't tried any yet.
Be prepared for the fact that you will not find the ideal fixture, compromise is often inevitable, or if you do find the perfect fixture, it will be horribly expensive. Selecting fixtures can be agonizing or fun. Try to have fun.