Some people will probably recommend the H440 or Define R5, and they are good-ish cases, but they are really bad for airflow. If you are already having airflow issues, moving to one of those two cases is not going to be much of an improvement, if it all. Also, they all cost around $100, but the Phanteks Enthoo Pro gives you the most case for your money. Another solid option with good airflow is the Corsair Air 540.
CPU Cooler, I honestly think there is no better option than the Cooler Master Nepton 240M for around $100. Nearly silent pump, incredibly high end included fans, so they don't need to be replaced, 5 year warranty, and it costs the standard ~$100.