24-bit (8-bit/channel) is sufficient but you will run into limitations depending on the extensiveness of your adjustments to contrast and tonality. In some cases you may even gain some posterizeation just from the conversion that you would not get with 48-bit editing although those situations aren't too common with good conversion technique.
That being said I find the Channel mixer provides the best conversions within PS short of a specialized plugin. You can get the Channel Mixer and curves for PSE from
this site which should save you from having to convert to 24-bit.