Most mosses do pretty well in low light, not just Java. Suesswassertang (not "truly" a moss but still gets lumped in with them), Pellia (same sort of thing), Flame, and Christmas mosses are some other options to consider.
While it is true that growth rate is directly related to the amount of light, it is also true that anubias species won't grow as fast as Hygro species will in the same tank. That being said, I recommend stem plants, because they do tend to grow faster, and they are much more forgiving to noobs.
I recommend starting with Rotala, Wisteria, Temple Plant (or other Hygrophilas), and Anacharis as your stems. Then you can also throw some cryptocoryne species in there as well, because they can grow pretty fast too under lower light conditions.
Anubias will certainly be fine under low light, but you might not actually ever see them grow, or do anything, and they might be boring to you at first.