Excellent question, well worth asking, but kind of large. There are a lot of variables. How many birds? What breed. Stil . . . to get the conversation going . . .
Assume ten chicks of a standard laying/dual-purpose variety, Rocks Orps, Wyandottes and their ilk.
I haven't room for anything permanent by way of a brooder and make out very nicely with corrugated boxes. Some are cut from one end of a refrigerator carton. The best have been television and air conditioner cartons, as the lids can be folded down while the birds are small, but folded and taped up to add height as they learn to test their wings (but can still be let down for feeding, cleaning and coddling). The darlings will take flight at a surpisingly early age. If (not IF, you WILL) have one that finds its way to perch atop your waterer, it will use that as a hopping off point to get up over the edge of the box and go exploring. If that happens at too young an age and it can't get back to the heat, you may lose it.
A box 2-1/2 or 3 feet square on the bottom is more than adequate for ten or a few more chicks to get them to a size where they are feathered out to withstand ambient temps and ready for transfer to the coop.
Two things I'd add as tips for such a setup. The heatlamp -- do not rely on the clamp. I'm old enough to remember when those clamps could actually hold a lamp solidly where you put it. Nothing I've found lately is reliable. If your lamp/reflector is new, dump the clamp, take it right off. You should find a loop taped to the whole affair when you bring it home that will clip onto the ceramic from which to hang it. Rig something solid (I brood mine in the garage and use the open stringers) and hang the light by that loop. I hang mine from baling twine looped over the stringers. To reduce the brooder temp every few days, all I have to do is loosen my knot, yarn her up a few inches and tie it a little higher than it was.
For the bottom, chicks are notorious for scratching their litter into their water and feed, especially with the otherwise very handy quart- and gallon-size waterers. Once your'e sure (a day or two will tell) that thy're all drinking as they should, raise your waterer up a little above the litter. First step for me is usually to set it atop a couple pices of 2x4 laid on their flat sides. Later, I'll bridge the 2x4 s with a scrap of board or plywood larger than the base of the waterer, and put on top of that platform. It isn't much higher, but provides some distance around its perimeter to limit what gets kicked/sctratched into it.
Fill us in on breed(s) and number, and I expect you'll get a whole lot of good ideas and practices back to help answer your questions.