Well, it's really up to you. While a smaller tank may present a more difficult challenge, it's certainly not impossible if you are diligent with maintenance. I have seen many nano tanks beautifully maintained even in such a small space. With a larger setup, you're going to have more stability (again, with constant maintenance) than a smaller size, and it gives you more room for live rock and corals later on; it also gives the fish some more room.
As far as needing all the equipment from the biocube, i would keep most of it (a list would be good to see). The lighting is not as crucial in this stage, though it does help with corraline algae growth. If you grow corals later on, you are most likely going to need a update for some serious lights.
Good luck, and post pics!
*Also, any idea what you are doing for clean up crew yet? I would suggest no sea cucumbers, nudibranches (seaslugs, or sea slugs), or sea stars; as they do well in larger tanks, but will quickly starve and die in small tanks like a 15 or 25 gallon. Snails and hermits work well, and some crabs will work, like emerald greens, but with the hermits and crabs, individual temperment may vary.