If you want to finish the basement you have to apply for the permit and meet all basic building, electrical, plumbing (if you have a bathroom) and fire code requirements for a habitable basement.
If you just want paint the foundation walls, throw down some carpeting, etc you don't need anything. As the heating goes, you can tap into existing ducts (if you have a forced hot air system) that will give you some heat down there just make sure your furnace can handle additional heating space...or you can add electric baseboard heat and if you want to add some outlets or lights you will also need a permit to make sure it's done right... Just keep in mind using electric baseboard, you have to calculate the area and make sure you install the right size baseboard to handle the area or if baseboards undersized they will run constantly and you end up with a huge bill.
That said, basements are usually comfortable in the winter and cool in the summer so most people who don't mind just having foundation walls painted don't usually add any heating down there. But you should have some sort of an air exchange, if you go by code you have to have a window opening area to be equal to 4% of the floor area that is the requirement or you have to provide mechanical ventilation system capable of providing 0.35 air exchanges per hour.
Good luck
Q
