What sort of nucleophile does NADH supply?

Hydride ion

Explanation:

You often see the reduction with NADH written as

NADH ⟶ NAD⁺ + H⁺ + 2e⁻

If you think about it, H⁺ + 2e⁻ is equivalent to H:⁻, so we could write the reaction as

NADH ⟶ NAD⁺ + H:⁻

In terms of a mechanism, the dihydropyridine ring of NADH transfers a hydrogen atom with its pair of electrons (a hydride ion) to the substrate and becomes the more stable, aromatic pyridinium ion in NAD⁺.