I currently use t-5 ho on one tank and MH on another. If you decide to go with a BTA, you would be fine with t-5 ho with 4 bulbs. Although more expensive, t-5 with individual reflectors make a significant difference in terms of light intensity. So I would recommend you get a fixture with those. I personally have a Tek light, though there are several brands that have the individual reflectors. As far as running carbon, you can simply hang a power filter on the back of the tank, I have a Hagen Aqua clear, there are lots of brands, and just put activated carbon in it. To be successful with an anemone and the fish you have, all the equipment you need is: a good light system, a filter (can be hang on, canister or internal power filter), a protein skimmer (which you have) a thermometer (keep water between 78-82F) and a couple of power heads for water circulation. I'm sure you already have the thermometer and power heads. You would want to cover the intakes of the powerheads with sponge filter to prevent your BTA from wandering into it (if you decide you want to go with an anemone). Water changes are the best way to maintain good water quality. It is a good idea to test your water weekly, a basic test kit that does ph, alkalinity, ammonia, nitrites, nitrates, and calcium. You could probably get by without worrying about Ca and alkalinity if you are diligent with your weekly water changes. Also, after the tank has cycled, you realistically will not need to check ammonia and nitrites.
I personally have used tap water successfully for many years, but perhaps I've just been lucky. Recently I did purchase a RO/DI unit and I like it. No observable changes in my aquariums, but it is an added safety to ensure control over the water used for water changes.
I think a good book, like Bob Fenner's The Conscientious Marine Aquarist is a good beginner's book. Also, RC and WetWebMedia are great resources for information. In the many years that I've been keeping fish (since I was about 5) I've had very few lfs personnel that really knew what they were talking about. There are some, but many just want to sell you stuff and don't know what they are talking about.
Also, what kind of substrate do you have? How much live rock do you have or do you plan to have?