The first thing that should go into the case are the Case fans if you are planning to put extra fans in.
Then install the CPU outside the case onto the Mobo. Now connect the RAM Modules onto the Mobo. Then Fix the Mobo into your case. After that, put the PSU in and fix it. Dont connect the cables yet.
Make sure the custome cooler has thermal component on its bottom. Else, put a single drop of a thermal compound you may have with you on the CPU surface exactly to the center of it. Then Fix the CPU Cooler onto the Mobo. Make sure the Thermal compound is spreading evenly. Do not move the Cooler over the paste on the CPU it will spread evenly if it is put properly on the center of the CPU surface.
Then start connecting the PSU power...