Cathy, from this point on, don't ask the LFS for ANY advise. They are either irresponsible or ignorant. Ich has a life cycle of 3 wks. Most of that time, the parasite is not even on fish, but IN YOUR TANK. Ich has what we call a "free-swimming" stage where, obviously, the parasite is swimming in your tank water [looking for fish to feed off of]. Knowing this, now you can see how all fish will become infected, sooner or later, if you introduce ich in to a closed system [aquarium]. Ich is highly contagious.
I'm going to recommend two very good books for beginners. Robert Fenner's, "The Conscientious Marine Aquarist", and Anthony Calfo/Robert Fenner's "Reef Invertebrates, an Essential Guide to Selection, Care and Compatibility". Both these books are great, easy reading and outstanding info for all hobbyists, but especially the inexperienced. The first book is a must have for beginners. If you only buy 1 hobby book then make it this one. The emphasis is on "conscientious" and the book places the reader/new hobbyists in the frame of mind to take good care of the animals we place in our tanks as well as make good hobby decisions. It covers A-Z and has very nice pics. The 2nd book is new and is the first in a series of books. It does emphasize invert selection, but it has a wealth of information about how to go about setting up a natural reef tank. It is excellent for someone trying to establish a reef tank. Outstanding pics.
Now to answer your question, yes you now need to leave your tank fishless for a month. Ich is a fish parasite and will die out in a tank without fish. Since the parasites’ life cycle is 3 wks, it should be taken care of within a month.
You can set up a 10 gal QT, a 20 gal long would be better. The bigger the tank, the more stable the environment, the larger the margin for error. However, you can do a 10 gal. If you set up a 10 gal, I would strongly recommend that you stick to small fish. With your size tank, larger fish are out anyway, yes, that includes tangs. A tang in that size tank just is not going to fare well. Tangs need “hard swimming room” which a small tank can not provide. However, clownfish would do well. There are a lot of beautiful reef fish that are on the smaller side and would look great in a small tank, and fare well as well.
What kind of lighting do you have? Anemones require strong lighting, preferably Metal Halide. In any case, placing an anemone in a tank that is just set up just is inappropriate.
Check out the nano forum here for some ideas on how to get started with your tank again. Also, visit the Reef Forum. How do you have the tank setup? Filters, powerheads, skimmer, etc.?
I’m sure you are very frustrated and disappointed right now, but you have come to a good place to get started learning. Don’t be scared off by more knowledgeable hobbyists here, and if anyone shows off by making fun of your lack of knowledge, don’t be afraid to hit the report to mod button. We have little tolerance for show-offs here. This is a place to learn and help out. All of us made some big mistakes when we were new to the hobby; believe me you are not the first to blunder.