The bases are oriented perpendicular to the helix axis. They are hydrophobic in the direction perpendicular to the plane of the bases (cannot form hydrogen bonds with water). The interaction energy between two bases in a double-helical structure is therefore a combination of hydrogen-bonding between complementary bases, and hydrophobic interactions between the neighboring stacks of base-pairs.
Even in the single-stranded state, the bases prefer to be stacked (like the steps of a spiral staircase if the bases are identical) and a single-stranded chain can also have regions of helical conformation.
The backbone of polynucleotides are highly charged (1 unit negative charge for each phosphate group; 2 negative charges per base-pair). If there is no salt in the surrounding medium, there is a strong repulsion between the two strands and they will fall apart. Therefore counter-ions are essential for the double-helical structure. Counter-ions shield the charges on the sugar-phosphate backbone. They may also contribute to an attractive interaction from fluctuating counter-ions around the backbone, similar to the Van der Waals interactions for fluctuating induced dipoles.