Clown anemones do not NEED supplemental feeding as long as they are healthy and you have bright lighting. Anemones have been shown to grow from small to quite large sizes without supplemental feeding (though they may grab stuff out of the water column particularly if you feed fish heavily). Limiting supplemental feeding may restrict/slow growth rates of anemones if you wish to keep them smaller in your tank.
However... there are benefits to supplemental feeding. They will grow faster and they may reproduce more frequently (sexually and asexually). Additionally, if an anemone is stressed or bleached, supplemental feeding can help provide an anemone with energy while it recovers.
People have many opinions about "best" anemone foods. In the wild, clown anemones are opportunistic feeders and will eat fish, clams, snails, crabs, shrimp, sea urchins, and for all intents and purposes anything that they can swallow. The important thing to consider when feeding:
(1) Large chunks of food take more time and energy to digest than small chunks of food. Generally, smaller feedings more often is much better for the anemone, to say nothing about ammonia spikes in your tank.
(2) Anemones are quite happy eating prepared marine foods. They do not "need" raw food to be healthy. If you prefer to feed raw foods, be VERY cautious about food poisoning. Do not feed anything raw that you would not eat yourself. If it looks or smells bad, DO NOT USE IT. There have been numerous anecdotes on this site of people who had a long-lived anemone in their tanks, and one night fed a questionable piece of food, and the anemone was dead in 12 hours.