they might take to one, butthey don't need one to be happy. I see your experience is listed as 1 month, meaning your tank can't be much older right? An anemone is a hard to keep animal, that requires a tank that has been running for a year or more, and has very stable water conditions, and intense lighting. They are not a good purchase for someone that is new to the hobby. Here is a very good article to educate you about anemones and thier needs.
http://www.carlosreef.com/AnemoneFAQ.pdf
Also the other corals you have listed are really going to be touch and go trying to keep them alive in that new of a system. What type of lighting do you have on the tank? What type of filtration (sump/fuge, over the back filter, skimmer) ? Keeping a reef tank takes lots of patience as far as getting it set up the way you think it should be. It can take years to build a reef, just like in the ocean. NOTHING good come quick in this hobby. The only quick things are hair algae blooms, disease, and equipment failure. Everything else takes lots of time. Most of the really pretty corals need an established tank of a year or more to thrive. You should start with easier to keep corals, like mushrooms and polyp, them slowly as your tank matures, you can add the harder to keep corals. Anything that is a filter feeder will need a mature tank. Until the tank has matured all you can offer is light and water for the most part. There are suppliments, but they are just that (suppliments). They also need the natural bio diversity that comes with a mature tank to get everything they need to survive.
If you have a question about any corals that you may want, as to if they will be ok in a newer tank, ask here on the forum, and AVOID impulse purchases. Always take any info from a local fish store with a grain of salt. Remember, they are trying to sell you anything you will buy. The people here on the forum are here to help, and have nothing to gain.
Good luck and WELCOME to our nightmare i mean hobby
