Hey there!
Welcome to the forums! I hope you enjoy your stay!
Thank you also for taking the time to do some research and ask some questions before getting started with harder corals.
Before you invest in purchasing some corals, try to invest in a new lighting system. A 36" long tank such as yours is pretty easy to light. A Nova Extreme lighting fixture from Pet Mountain dot com is only $76.18 with free shipping... and it comes with two new bulbs to help get you started. That's a small price to pay for the health of your new corals!
With the new lighting fixture you will be able to keep corals such as kenya trees, colt corals, leather corals, green star polyps, blue anthellia, anthellia, xenia, zoanthids, protopalythoas, a wide variety of mushrooms: hairy green mushrooms, ricordeas, all different colors. I wouldn't try nepthea as suggested with that lighting. As suggested too, you could try some easy non-photosynthetic corals, however you must have a top of the line filtration system to be able to feed your tank and corals enough for them to survive.
Of course, even with this new lighting, I would suggest to keep most of your new additions within the top half of the tank.
I wish you the best of luck and hope to see you around!