Brittle and serpent stars would be fine in your tank as long as you provide them with occasional meaty bits of food. They're mostly scavengers and most species will very rarely cause any problems in a reef tank. However, most are very shy and will spend most of the day hidden. You won't usually see anything more than an arm or two during the day unless you entice them out with food.
The true sea stars can be pretty much lumped into two groups- those that aren't reef safe and those whose diet is unknown or can't be met in captivity. Linckia and Fromia are the two most common reef safe stars and neither of their diets are known. Both are presumed to feed on some component of the thin layer of film that grows on solid surfaces in tanks. This means they need a lot of well established rock to graze. As a result, in small tanks they usually last less than the 18 months it takes them to starve- and yes, that includes the half-dollar sized Fromia. The only species that really even stands a chance at long term survival in a 55 is Linckia multifora, and even that is borderline in a mature tank of your size.
Sand sifting stars are NOT a good choice for captivity. There are several species sold under that name with various diets, but all feed in part or in whole on sandbed fauna, which does more harm to the tank than good. In most tanks, the sandbed also cannot support large enough populations of these animals to feed these stars long-term.
In general sea stars are poor shippers and very sensitive to poor acclimation or changes in salinity. It's hard to find healthy specimens to begin with and of those, very few make it to the two year mark due to difficulty keeping them fed.