Installing insulation in the wall cavities between the studs is necessary if you want your finished basement to feel warm. You have several choices in the type of insulation you choose. Friction fit fiberglass insulation with an R-value of about R-15 has been used for years. It comes in batts that fit between the studs in your walls and are held in place simply by friction. Each batt is 3-inches thick, which is why you left that extra inch when positioning your wall studs. Because this type of insulation is fiberglass, it can be placed around the wiring and electrical outlets without the risk of causing a fire.
The insulation should be installed from the floor right to the ceiling to ensure you don't end up with any cold air spaces behind your walls that will make your room uncomfortable. The fiberglass is light and easy to work with, plus it can be cut with a straight edge and a utility knife. Wear gloves and a long-sleeved shirt when working with the fiberglass batts; the fibers can be quite itchy on your skin.
One alternative insulation you can use in your basement walls is polystyrene foam. It comes in large sheets (24x96-inches) and needs to be cut to fit between the studs. All that is usually necessary is a small handsaw. Polystyrene doesn't provide the same R-value as fiberglass, but its proponents feel it is better to use in a basement because it is impervious to water and moisture.
Whatever type of insulation you choose, don't neglect to install a vapor barrier over it. A vapor barrier's function is to prevent the movement of warm moist air from the heated interior of the home into the cooler areas in the wall cavity. If air migration is allowed, the warm air would cool and its moisture would be left behind in the wall cavity, where it could cause wood rot as well as mold and mildew.
A vapor barrier is installed on the inside of the insulation closest to the interior surface. The best vapor barrier is a polyethylene plastic sheet spread over the studs and stapled in place. Overlap any seams with at least one row of studs to make sure no moist air can enter the wall cavity. For extra safety, tape all the seams.