It depends on what you use your basement for and if the present one is adequate. Most HVAC people install a unit big enough to handle the basement with the rest of the house. Some put in duct work and wait on the returns and some don't put any ductwork or returns and wait until you layout and finish the basement.
One unit in house = one thermostat on main floor. If no one is living in the basement then one would be OK, would keep it comfortable by adjusting the registers, and remember heat rises so it helps heat the rest of the house.
If you have a sleeper in the basement, then a second unit would act like a separate zone for the basement so the occupants could control their own heat. It takes it own duct work. If you crank up the heat for the second floor, then no affect on basement.(except with one furnace you can still balance the registers which doesn't always work that well)
Fireplace, IMHO, will have little effect. You won't burn all day every day, just a few hours on some evenings. Wood gets expensive and doesn't heat the entire basement all that well. A bad drafting fireplace will fill your house up with smoke(use one that uses all fresh air).
It boils down to use, your expected comfort level, and how much you want to spend. Cheapest is to add some ducts and returns. Good luck.