Where are you brooding, in a climate-controlled area or outside with changing temperatures. That has a lot to do with how you manage heat. I brood in a 3' x 6' brooder outside in the coop where the temperature can go from freezing to 70 F in a day. I use a heat lamp and keep one corner toasty in the coldest temperatures and let the rest cool off to ambient so they can find a comfortable temperature.
I don't like using a heat lamp inside. You can use lower wattage bulbs to keep the heat lower but with space typically limited you still have a tendency to overheat them. People have been using heat lamps for over 100 years, not just to keep chicks warm. I do not use that clamp to attach it, I use wire or chain so it cannot fall. I haven't had a problem. If you don't use it properly, they can be a fire risk but then so can anything electrical. Check the CDC reports on deaths and burns from heating pads. If used properly heating pads are really safe.
My brooder has a wire bottom. I elevate it so the poop drops through, keeps the brooder clean and makes it easy to clean up the poop. That might make a mess if you are brooding in your house.
In winter I put a piece of plywood on the wire under the heat. That helps keep them warmer. To clean, I tilt the plywood and brush it off through the wire bottom. If you want to put hay, straw, wood shavings, or other bedding in there you can. Nothing wrong with that at all, you just have to manage keeping it clean.
Other than keeping one area warm enough in the coldest conditions and an area cool enough in the warmest conditions I don't have a lot of rules for brooders. Well, I try to not over crowd them. That can lead to behavioral issues.
Yes, slick surfaces like cardboard or newspaper can cause leg problems. Some people put paper towels down, they are not slick.
Good luck!