I definitely like the idea of an anemone tank. Those lights should be more than enough. I would wait for your tank to settle in before adding any nems though.
As far as filtration, rather than a skimmer, look into the media baskets that inTank offers. I have one with chaeto in the bottom chamber that is lit with the JBJ magnetic fuge light and it grows ridiculously well! I've tried different skimmers on my cube and can honestly say there doesn't seem to be any benefits to one of these setups. Just stay current with your PWCs each week (4-5 gallons) and you'll be fine. Mine has been at 0 nitrates since I added the chaeto.
Looking forward to this build!