For detailed R value recommendations, search keyword "R-Value" for the title "WHAT ARE THE RECOMMENDED INSULATION LEVELS?".
Note that in the previous answer, some of the common options for basement insulation does not even meet the minimum recommendation of RSI - 2.1 (R-12). Manufactures of all the products are now claiming availability of their respective panels in thickness up to RSI - 3.5 (R-20), but more than 2 inches of any of the products if pretty hard to find in a real live down on the corner store. You could laminate panels together, or strap one to the horizontally and then strap another over it vertically, or create inside/outside combinations to obtain the desired insulation levels.
When less than 50 percent of a basement's height is below ground, the walls should be treated as ordinary, above-ground walls, because the earth is no longer adding its own special insulating effect. In this case, the foundations should be treated as slab-on-grade, to avoid frost heaving problems. (search keyword "Slab-On-Grade" for the title " HOW DO I INSULATE SLABS ON GRADE?")