ARCTIC Liquid Freezer III 360

ARCTIC Liquid Freezer III 420 is one of the best choice with a budget price.

For that processor, opt for a 280mm or 360mm cooler. While a 240mm might work, it'll be constantly strained. A 280mm AIO is the safer choice, providing better cooling performance without excessive stress.

Consider the Lian Li Galahad 360 II - solid performer at a good price point. The 360mm rad is what you want for the 13900K's heat output. Make sure you've got good case airflow too, as these chips run hot regardless of cooling.