In a 3 gallon tank, java fern, anubias, and any rotala are going to be background plants, if they fit. HM probably won't grow well in 3 wpg on a 3g tank. Those little tanks take a lot of light to grow medium - high light plants.
The java moss will look great, though! I have never tried this with moss, just riccia, but a great, cheap net you can use is tule from a craft store. It won't rot, it's extremely cheap, and you can get it in dark green, so you won't even notice it
