green star polyps are quick reproducers, so once you get them, your pretty much stuck with them. Mushrooms, and xenia, the same only a little less speed with spreading.
try a LPS frag. I say frag so you dont spend to much. Frogspawn and torches would be a good start. Or if you like the hammer, try that.
do your best to assure that they are aqua-cultured, the will have a better success rate.
If you do decide to get an LPS, know how to, and what to feed them, because it is benficial to them.