First and most important question: are you cycled?
If no, then you'll want to be testing the water each day to watch your cycle. Even though you used Biospira you might have a small cycle. I used it and I had a small cycle that lasted just over a week. You should be able to see the ammonia and nitrates/nitrites rise and then fall and the start of diatoms usually signals the tail end of the cycle. When they're all at 0 you can safely add coral, but I'd add a clean-up crew first to get rid of the diatoms and prevent more algae.
If yes, you are cycled, then you should be able to add corals right away. Whatever you add make sure to put it near the bottom of the tank and then gradually move it up over a few days time to where you want it so it can get use to your lights (unless it's SPS, I'm not sure how to add those).
For the bubble-tipped anemone I'm not sure if a 20 gallon is big enough for that type; definately not for a rose tip. I'm sure someone else will chime in if I'm wrong. Also, clownfish don't need an anemone, but they do seem more lively if they manage to host one. Sometimes they'll host LPS corals like torch and hammer corals, so you can always get one of those as an alternative.
As for additional fish you'd want to look for something that is relatively small as you'll probably only be able to add one other fish to the tank, but will want to make sure it can stand up to the clowns if they get territorial. A clean-up crew is always good to add as well, such as snails and hermit crabs, and a shrimp might do well in the tank too.
And lastly, welcome to AA!
