Doug has given you some good advice. I will add to it. Forget about an anemone. Their lifespan in the wild is so long it is undetermined. Their lifespan in a tank is generaly under 2 years, most perish long before that.
After the ammonia and nitrite are reading ZERO you should do a 30% - 50% water change. That will bring the nitrates down to acceptable levels. Add a pinch of food and test a week later to make sure there is still no detectable ammonia or nitrite. Then you are ready to add your first fish.
A bit of advice (my 10 rules) for a succesful aqaurium or, things I learned the hard way!
Rule # 1. Nothing Good ever happens Fast in a salt water aquarium
Rule # 2. Don't add anything (supplements/chemicals/minerals)you don't test for first.
Rule # 3. PWC
(Partial Water Changes) are your friend, and cure many ills.
Rule # 4. QT EVERYTHING before adding it to your tank (mandarins excepted, corals should be dipped)
Rule # 5. Use only RO
water (either buy it or make it)
Rule # 6. All animal species live longer on a 30% reduced caloric intake. Only feed every other day at most (fish species dependant)
Rule # 7. Hyposalinity is the best, safest, and most effective treatment for marine Ich (IMHO
Rule # 8. A Refractometer is a MUST HAVE, not a luxury.
Rule # 9. Anemones will never live anywhere near their normal (aprox 30 years) lifespan in a home aquarium. Leave them in the ocean.
Rule # 10. The tank size recommendations for fish are there for a reason - HEED THEM!