The height is more important when determining the amount of lighting you need. More height needs more light to penetrate the water.
Java ferns are low light plants, so on a standard 15 gallon a normal fluorescent should be fine. You will need the correct spectrum so a plant bulb would be best (5000-6000 k spectrum. It's cheaper to buy a normal 5000k bulb than buy a light specifically marketed for aquarium plants.). On the down side a plant bulb is a horrible color for actual viewing (it tends to make a pinkish light). A lot of people use a plant bulb along with a brighter bulb so the plants will still have enough light and the correct spectrum, but better for viewing the fish. If you have too MUCH light you will have horrible algae growth.
You will want to leave your light on for about 8 hrs a day, you may want a timer. If you leave it on too long you will also get algae.
Java ferns are hardy plants so you don't need to go overkill.
If you have a 15g high tank you will need more light to penetrate the water depth.
As long as you have a fluorescent light though you should be fine. At worst the plants won't grow quickly, but they will likely stay alive.
On a side note, goldfish sometimes like to eat plants, so your java ferns may be consumed or injured. You'll just have to see.
BTW, 15 gallons is a bit small for goldfish (even one goldfish is probably too many) so you will likely have to upgrade in the long run for the health of your fish.