The goal should be getting nitrates down to zero. I don't think a skimmer alone will accomplish that. To do this you need to remove the nitrates (by water changes or cheato) and limit what you are adding. Feed your fish less food more often so they eat every crumb. Any feeding of the anenome should be target fed with a turkey baster so all the food goes to the anenome, you can also put a container over the anenome while feeding so that all the food stays in close proximity.
The problem you will really be fighting is you need to feed the anemone, but you also need to lower nitrates. Sort of a rock and a hard place, so you need a good export strategy such as a skimmer and/or cheato. I would research the cheato idea as it did wonders for my tank, but I have a sump full of the stuff. When you do water changes use a tooth brush and scrub the rocks and siphon out what comes off the rocks. It is sort of a challenge but you can hold the hose end and toothbrush in one hand and it really works pretty good, this will help remove stuff before it becomes nitrates.
-chris