well in general most require high flow (like an SPS coral tank would have), lots of swimming space for more than one (some do better in herims of a male to multiple female but mostly its just cool to keep them that way but being a herim space is needed due to aggression as they jockey for their place in it.), require feeding several times a day which if you have four like I do means filtering has to be up to par. Many are finicky eaters. mine wont touch dry food and lyretails are the easier ones to feed. Mine only eat frozen or live mysis, reef plankton. sweetwater plankton (daphnia) and brine.
The only anthias considered relatively easy/hardy to keep are Lyretail and bartletts. painted, square spot, dispar, bicolor are considered keepable but harder. give or take a few the rest dont usually do well in captivity.