The main advantage of a rigid fork on a SS is that the bike will be more stable when you stand up and mash. With any suspension on the bike, part of your pedaling energy will go into compressing the suspension and the bobbing motion will make things harder for you. Other advantages: lighter, cheaper, simpler, sharper cornering, develops added skills. Disadvantages: will hurt/numb/fatigue your hands/arms on real rough terrain over extended periods, may not save you on a botched landing or overzealous run down a bumpy descent.
I think it mainly depends on terrain and the ultimate is to have both a rigid and boingy fork to switch out for different trails. Start out rigid, though, so you don't get spoiled.