White-rot fungi can degrade a wide spectrum of environmental pollutants, including pharmaceuticals, which are not efficiently removed from wastewater by conventional methods, e.g., the activated sludge method. However, the treatment of wastewater with the use of fungal cultures (mycoremediation) also has significant limitations: among others, the need to use appropriate, often-expensive culture media. We aimed to screen 18 media ingredients, including seven agrifood byproducts for Armillaria mellea, Phanerochaete chrysosporium and Pleurotus ostreatus in submerged cultures to select the low-cost medium optimal for biomass production and laccase activity. We screened nine mathematic models to describe the relation of fungal growth and the amount of the selected byproduct in media. Finally, we tested the ability of the strain with the highest mycelial growth and enzyme-producing ability in the selected medium to degrade eight drug contaminants. Three media variants composed of byproducts provided both efficient growth and laccase production: corn steep liquor + poplar, dried distillers grains with solubles + poplar and corn steep liquor 50%. Among the investigated growth models, the Han–Levenspiel equation described well the specific growth rate in function of the nominal substrate concentration in one-component media. Pleurotus ostreatus, the fungus with the highest ligninolytic enzyme activity, cultured in medium composed of corn steep liquor, removed six of eight drug contaminants with a removal degree of 20–90% in 48 h. The obtained data on the optimal culture media consisting of insoluble components provide initial data for upscaling the process and designing an appropriate type of bioreactor for the process of removing drug contaminants from water.