I use a Scythe Fuma 2 with my 5900X and it works quite well. That should fit in that case, it doesn't have issues with RAM clearance due to its design, and it costs around $60-70. I wouldn't recommend anything lower-end for a 5900X, especially given the lackluster airflow of your case.
Given the lackluster airflow, you may want to go with an 240mm AIO cooler in the front of the case so that you have more heat-soak. The Arctic Liquid Freezer II 240 tends to cost around $110-130, and it's a good quality cooler. You could also consider the Cooler Master ML 240 or Enermax LIQMAX III 240, which tend to be cheaper, around $75-100, but aren't as good.