The type of anemone you can start out with greatly depends on the type of tank you have, the lighting, and the water flow. The are probably something you don't want to start putting in your tank right away without having your feet wet with saltwater tanks. Carpet anemones are far from being small. The
Anemone FAQ has tons of info on Anemones, here is what it had to say on difficulty requirements:
DIFFICULT
E. quadricolor (bulb-tentacle anemone, BTA, or corn anemone)
S. haddoni (haddon's sea anemone, saddleback anemone, carpet anemone, or sand carpet)
MORE DIFFICULT
M. doreensis (long tentacle anemone, LTA, or corkscrew tentacle sea anemone)
C. adhaesivum (adhesive sea anemone or pizza anemone)
H. aurora (beaded sea anemone or sand anemone)
H. crispa (long tentacle anemone, LTA, leathery sea anemone, or milk anemone)
H. malu (sebae anemone, delicate sea anemone, or sand anemone)
MOST DIFFICULT
H. magnifica (magnificent sea anemone, ritteri, or skunk anemone)
S. gigantea (gigantic sea anemone or carpet anemone)