x2. Use the space you have and don't bother with buying tubs or whatnot which won't last long as a brooder. Something as simple as 3' cardboard stapled or taped to the wall of the coop to make an "enclosure" should work fine for about the first 2 weeks (after that they'll easily be able to get over it but will be ready to utilize all the space anyhow), or if you want to get fancier you can take hardware cloth and screw it into the walls/beams to portion off part of the coop.
I'm very simple with food and water, I just have a plastic mason jar size feeder and waterer sitting up on bricks or scrap wood to keep them out of the bedding. I don't have issues with water getting knocked over because I find that as long as chicks have ample room to move around as they grow, they don't tend to knock into things the way they would in a smaller space.
I use a mama heating pad for heat. For 15 birds you may need 2 pads or plates depending on size. If you plan on sticking with the heat lamp, make sure it is WELL secured (do NOT rely on the clamp to hold it up, it should be clamped, hung by the loop at back of the lamp, and even the cord should be looped over the support beam) and have the lamp only on one side of the brooding space so chicks have the option of getting away from heat when they don't want it.