NO! You can use the size bulb that will keep your particular brooder warm as prescribed. When I have them in a small one sometimes a small wattage will keep it warm and sometimes in the larger one I use the 110w brooder light. Do a dry run with a thermometer on the bottom of your brooder with a light overnight. It its to warm lift the bulb some if too cool you may want to use a larger wattage bulb.
That depends upon what you are using for a brooder. Many folks here use small bins or hutches for a few chicks and keep them inside the house, basement, or garage. It is fairly easy to provide enough heat to a few chicks in those types of setups with a regular light bulb.
Traditionally, chicks were brooded inside a ring on the floor of an unheated barn or outbuilding. Those are the conditions where a heat lamp comes in handy. The first chicks we had, I brooded them early in the spring in a ring on the garage floor and used a 250 watt heat lamp. Later batches were brooded on an open-air, screened porch on the back of our house in 50 deg plus weather. The heat lamp worked fine even though it was an open, breezy porch. I just used a high ring to keep the breeze off of the chicks.
I have a outside brooder and normally use 100-250w regular bulb. This time I tried a 100w halogen bulb and it worked fine too. I honestly don't set mine up like everyone says to, I just got my on way because I had to teach myself with no internet to look it up on.
It's all a matter of how many chicks, the ambient temperature, and how drafty it is around your brooder. Right now I have a 250 and a 125 brooder light in my hover. But the brooder box it's in is in an open bay of my shop and it's been going to freezing or below every night. In another week or so I'll swap out the 250 for another 125 when they don't need quite so much heat. Because the brooder is outside I never use just one bulb in case one should burn out. When they're about four weeks I'll go to a pair of 100 watt bulbs then eventually down to a pair of sixties before I take the hover out altogether.
In an area that is more sheltered and climate controlled you can use lower wattages from the beginning.
I brood in an outdoor outbuilding (it's small and insulated) I have a 250 watt red heat lamp, but recently I found a 100 watt red halogen bulb. (it's meant as an outdoor light, got it at home depot) I lowered it and it keeps the brooder at 70 degrees right now. (we're in CA though, so we have fairly mild weather, it's been in the high 30's at night)