I don't keep mine in either. A lot of people believe that you should not remove them until the entire hatch is complete and the last chick is dry. I leave mine in for a few hours to get warmed up and find their feet, but unless I have a lot of others that have pipped I move mine to the brooder after a few hours. They can stay in the bator up to 3 days if necessary, but there is no reason to keep them in that long especially if all your eggs have hatched.
Your brooder should be warmed at one end to 95 degrees before you put them in. General rule is you decrease the temp 5 degrees every week till you are at room temp. The chicks will move in and out from under the light as they need. They are pretty good at taking care of their warming needs, however, if they are huddled together underneath the light and are squaking and unhappy, it is not warm enough for them.
They need to start feed on starter crumbles once in the brooder and they need to have it and water available at all times. When you put the chicks in the brooder it is recommended to dip their beak in the water so they will know how to find it quicker. Depending on what type of water dish you have you may want to consider putting sterile rocks or marbles in it to keep them from drowning themselves. Also if you have it or have a place to get it you may want to consider putting some sav a chick in the water the first 2-3 days.
Congrats on the hatchers!