A Red filter is aimed at filtering the Blue color of the water and thus returning the red colors lost in the water.
Most Red filters will be perfect for 30-45ft (10-15mts) of depth. However, deeper than that, it won’t be sufficient and shallower, it might be too strong.
Most DSLR and Mirrorless camera shooters (or even advanced compacts) do not use a Red filter, unless going for a specific wreck dive or planned ambient light reef scene. Instead they shoot RAW and therefore allow changing the white balance of the image while processing on the computer with no loss of clarity.
Post processing the pictures this way will create a more accurate white balance per image. The downside is that it will take time.
Lighting such as strobes or video lights completely replace the need for a filter, for most subjects. Very rarely would you combine a red filter with a light, as this would usually result in red subjects. Red filters are very efficient when shooting with ambient light and are a great tool for videos. Just remember to remove them when turning on your lights or strobes!