You can have a healthy tank without plants, plants just make it a little easier. Fertilizer shouldn't mess up your cycle, but if you want to wait to add fertilizer until your cycle is done, that is okay. The anubias and java fern are slow growing plants and it might take weeks for them to show the effect of no fertilizer so if you decide not to fertilize you won't kill them, they just won't grow. (You do know not to plant these with the roots is the substrate right? Tie them to a rock of piece of wood using fishing line/super glue gel/cotton thread. Moss looks good glued/tied to a rock too)
Your plants probably look really tiny and not all that great right now. They are slow growers and if anything like my java fern when I bought it, only have two or three leaves. I experimented wiht my java fern/windelov fern (a kind of java fern where the leaves split on the end). I stuck my plain java fern, came with 3 leaves,in the shadiest corner of the tank. It didn't die, but it didn't grow either. The windelov fern only had 3 leaves, stuck it in the middle of the tank, and it grew really wide, bushy leaves and looks gorgeous. moved the plain java fern beside it and now it is starting to grow more leaves.
Don't be afraid to rearrange your plants and move them around. (it's easiest with the plants that need tied to something.)
Also, most plants that are shipped to pet stores are grown with their leaves out of water, because most plants grow best if part sticks out of the water. This is not true for java ferns. When treated like this, the ends of the leaves die and go black. So if your java fern has black tips, wait until it has two or three new leaves that are the size of the original leaves, and you can cut off the ugly black tipped leaves.