I like to brood where ever the chicks are going to be living. I've brooded in a coop and a tractor that I've used as a grow-out pen. As long as they have something for a draft shield when they're really young, I can adjust the height of the lamp to get whatever temperature I need. Later, they just have the heat lamp until they feathered out. They can come and go underneath it when they want and have the run of the place. If I'm raising them in warmer weather, they don't even need that for long.
I don't have a rodent problem in the coop. I don't feed outside, only in the coop. I think the thing that really helps is that I have an elevated pop hole door. It's quite high up and the ramp is a long one. It's also an open grate design, not solid. Rodents would have to go to the middle of the run to get on the end of the ramp. That's a lot of exposure. Running along the outside of the coop wall and just popping in an open door is a very inviting way in. We do have trouble with rodents on the other side of the property going into our pole shed and there's not even any food over there. They just walk right in. The cat's hunt in there, which helps.
What I really need is somebody that eats ground squirrels/chipmunks. They mess with the garden seeds and make annoying noise right outside the door. I don't care if they live around here, I just want them to live up farther in the woods.