Going to try and help although it would be nice for some additional info. You said its your first algae breakout? I assume that means its a very new tank.
The green algae you see is normal, and you will see that with a cycling tank. You can put some CUC in there but its not really nessecary as it will leave once things stabilize.
Typically purple algae is Coraline algae and its safe. If it is hard and attached to your glass / rock work chances are its that. You want to see it
The brown algae you are talking about sounds like diatoms to me. Crabs eat it, also some fish also eat it. Again, this will leave once everything is stable. However if you want to get rid of it throw some hermits on it, maybe a sea cucumber to churn the sand for you. fighting conch snails are great for churning the sand as well.
I am unsure of what the white algae is... Perhaps a pic? Could be a sponge.
That being said, it would be helpful if next time you included:
total tank cycle time. (how long its been up)
water parameters. (ammonia, nitrate, phosphate etc)
possibly pictures?